A Homology Theory for Smale Spaces

A Homology Theory for Smale Spaces

Author: Ian F. Putnam

Publisher: American Mathematical Soc.

Published: 2014-09-29

Total Pages: 136

ISBN-13: 1470409097

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The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.


Book Synopsis A Homology Theory for Smale Spaces by : Ian F. Putnam

Download or read book A Homology Theory for Smale Spaces written by Ian F. Putnam and published by American Mathematical Soc.. This book was released on 2014-09-29 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces

Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces

Author: Valerio Proietti

Publisher:

Published: 2020

Total Pages: 0

ISBN-13:

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Book Synopsis Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces by : Valerio Proietti

Download or read book Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces written by Valerio Proietti and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Intersection Homology Theory

An Introduction to Intersection Homology Theory

Author: Frances Clare Kirwan

Publisher: Halsted Press

Published: 1988

Total Pages: 169

ISBN-13: 9780470211984

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Book Synopsis An Introduction to Intersection Homology Theory by : Frances Clare Kirwan

Download or read book An Introduction to Intersection Homology Theory written by Frances Clare Kirwan and published by Halsted Press. This book was released on 1988 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Operator Algebras and Applications

Operator Algebras and Applications

Author: Toke M. Carlsen

Publisher: Springer

Published: 2016-07-30

Total Pages: 348

ISBN-13: 3319392867

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Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.


Book Synopsis Operator Algebras and Applications by : Toke M. Carlsen

Download or read book Operator Algebras and Applications written by Toke M. Carlsen and published by Springer. This book was released on 2016-07-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.

A HOMOLOGY THEORY FOR MULTIPLE CONNECTED CONTIGUOUS POINT SPACES.

A HOMOLOGY THEORY FOR MULTIPLE CONNECTED CONTIGUOUS POINT SPACES.

Author: KATHLEEN E. BUTCHER

Publisher:

Published: 1946

Total Pages: 188

ISBN-13:

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Book Synopsis A HOMOLOGY THEORY FOR MULTIPLE CONNECTED CONTIGUOUS POINT SPACES. by : KATHLEEN E. BUTCHER

Download or read book A HOMOLOGY THEORY FOR MULTIPLE CONNECTED CONTIGUOUS POINT SPACES. written by KATHLEEN E. BUTCHER and published by . This book was released on 1946 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach

Author: Jochen Denzler

Publisher: American Mathematical Soc.

Published: 2015-02-06

Total Pages: 94

ISBN-13: 1470414082

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This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.


Book Synopsis Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach by : Jochen Denzler

Download or read book Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach written by Jochen Denzler and published by American Mathematical Soc.. This book was released on 2015-02-06 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.

Homology Theory

Homology Theory

Author: James W Vick

Publisher:

Published: 1994-01-07

Total Pages: 264

ISBN-13: 9781461208822

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Book Synopsis Homology Theory by : James W Vick

Download or read book Homology Theory written by James W Vick and published by . This book was released on 1994-01-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

2016 MATRIX Annals

2016 MATRIX Annals

Author: Jan de Gier

Publisher: Springer

Published: 2018-04-10

Total Pages: 656

ISBN-13: 3319722999

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MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.


Book Synopsis 2016 MATRIX Annals by : Jan de Gier

Download or read book 2016 MATRIX Annals written by Jan de Gier and published by Springer. This book was released on 2018-04-10 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

On the Differential Structure of Metric Measure Spaces and Applications

On the Differential Structure of Metric Measure Spaces and Applications

Author: Nicola Gigli

Publisher: American Mathematical Soc.

Published: 2015-06-26

Total Pages: 104

ISBN-13: 1470414201

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The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.


Book Synopsis On the Differential Structure of Metric Measure Spaces and Applications by : Nicola Gigli

Download or read book On the Differential Structure of Metric Measure Spaces and Applications written by Nicola Gigli and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Author: Gaëtan Chenevier

Publisher: American Mathematical Soc.

Published: 2015-08-21

Total Pages: 134

ISBN-13: 147041094X

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The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.


Book Synopsis Level One Algebraic Cusp Forms of Classical Groups of Small Rank by : Gaëtan Chenevier

Download or read book Level One Algebraic Cusp Forms of Classical Groups of Small Rank written by Gaëtan Chenevier and published by American Mathematical Soc.. This book was released on 2015-08-21 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.