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This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.
Book Synopsis The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2) by : John Guaschi
Download or read book The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2) written by John Guaschi and published by Springer. This book was released on 2018-11-03 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.
This volume presents the proceedings of the Joint Summer Research Conference on Algebraic K-theory held at the University of Washington in Seattle. High-quality surveys are written by leading experts in the field. Included is an up-to-date account of Voevodsky's proof of the Milnor conjecture relating the Milnor K-theory of fields to Galois cohomology. The book is intended for graduate students and research mathematicians interested in $K$-theory, algebraic geometry, and number theory.
Book Synopsis Algebraic $K$-Theory by : Wayne Raskind
Download or read book Algebraic $K$-Theory written by Wayne Raskind and published by American Mathematical Soc.. This book was released on 1999 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the Joint Summer Research Conference on Algebraic K-theory held at the University of Washington in Seattle. High-quality surveys are written by leading experts in the field. Included is an up-to-date account of Voevodsky's proof of the Milnor conjecture relating the Milnor K-theory of fields to Galois cohomology. The book is intended for graduate students and research mathematicians interested in $K$-theory, algebraic geometry, and number theory.
Book Synopsis The Whitehead Group and the Lower Algebraic K-theory of Braid Groups on S2 and RP2 by : Silvia Millan-Vossler
Download or read book The Whitehead Group and the Lower Algebraic K-theory of Braid Groups on S2 and RP2 written by Silvia Millan-Vossler and published by ProQuest. This book was released on 2008 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
Book Synopsis The $K$-book by : Charles A. Weibel
Download or read book The $K$-book written by Charles A. Weibel and published by American Mathematical Soc.. This book was released on 2013-06-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
Book Synopsis Algebraic K-Theory. Proceedings of a Conference Held at Oberwolfach, June 1980 by : R. Keith Dennis
Download or read book Algebraic K-Theory. Proceedings of a Conference Held at Oberwolfach, June 1980 written by R. Keith Dennis and published by Springer. This book was released on 2006-11-15 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic K-Theory. Evanston 1980 by : Eric Friedlander
Download or read book Algebraic K-Theory. Evanston 1980 written by Eric Friedlander and published by Springer. This book was released on 2006-11-15 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic K-theory written by and published by American Mathematical Soc.. This book was released on 1991 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Some Methods of Algebraic $K$-Theory by : Hyman Bass
Download or read book Introduction to Some Methods of Algebraic $K$-Theory written by Hyman Bass and published by American Mathematical Soc.. This book was released on 1974-12-31 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic K-theory written by V. Srinivas and published by Birkhauser. This book was released on 1991 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic K-theory by : R. Keith Dennis
Download or read book Algebraic K-theory written by R. Keith Dennis and published by Springer. This book was released on 1982 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: