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Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
Book Synopsis Algebraic and Geometric Topology by : R. James Milgram
Download or read book Algebraic and Geometric Topology written by R. James Milgram and published by American Mathematical Soc.. This book was released on 1978-12-31 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Book Synopsis Algebraic and Geometric Topology, Part 2 by : R. James Milgram
Download or read book Algebraic and Geometric Topology, Part 2 written by R. James Milgram and published by American Mathematical Soc.. This book was released on 1978 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Book Synopsis Algebraic and Geometric Topology by : R. James Milgram
Download or read book Algebraic and Geometric Topology written by R. James Milgram and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
Book Synopsis Algebraic and Geometric Topology, Part 1 by : R. James Milgram
Download or read book Algebraic and Geometric Topology, Part 1 written by R. James Milgram and published by American Mathematical Soc.. This book was released on 1978 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
Book Synopsis Topology and Geometry by : Glen E. Bredon
Download or read book Topology and Geometry written by Glen E. Bredon and published by Springer Science & Business Media. This book was released on 1993-06-24 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Book Synopsis Lecture Notes in Algebraic Topology by : James F. Davis
Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
Book Synopsis A Basic Course in Algebraic Topology by : William S. Massey
Download or read book A Basic Course in Algebraic Topology written by William S. Massey and published by Springer. This book was released on 2019-06-28 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.
The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.
Book Synopsis Geometric Topology: Localization, Periodicity and Galois Symmetry by : Dennis P. Sullivan
Download or read book Geometric Topology: Localization, Periodicity and Galois Symmetry written by Dennis P. Sullivan and published by Springer. This book was released on 2009-09-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.
This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.
Book Synopsis Geometric Aspects of General Topology by : Katsuro Sakai
Download or read book Geometric Aspects of General Topology written by Katsuro Sakai and published by Springer Science & Business Media. This book was released on 2013-07-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy.
Book Synopsis Algebraic and Geometric Topology by : Andrew Ranicki
Download or read book Algebraic and Geometric Topology written by Andrew Ranicki and published by . This book was released on 1985 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
