The Whitehead Group And The Lower Algebraic K Theory Of Braid Groups On S2 And Rp2
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The Lower Algebraic K Theory Of Virtually Cyclic Subgroups Of The Braid Groups Of The Sphere And Of Zb4 S2
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Author : John Guaschi
language : en
Publisher: Springer
Release Date : 2018-11-03
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 has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
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.
The Classification Of The Virtually Cyclic Subgroups Of The Sphere Braid Groups
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Author : Daciberg Lima Goncalves
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-08
The Classification Of The Virtually Cyclic Subgroups Of The Sphere Braid Groups written by Daciberg Lima Goncalves and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-08 with Mathematics categories.
This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks an important step in the computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysis of their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups. This manuscript will serve as a reference for the study of braid groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra.
The Whitehead Group And The Lower Algebraic K Theory Of Braid Groups On S2 And Rp2
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Author : Silvia Millan-Vossler
language : en
Publisher: ProQuest
Release Date : 2008
The Whitehead Group And The Lower Algebraic K Theory Of Braid Groups On S2 And Rp2 written by Silvia Millan-Vossler and has been published by ProQuest this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Braid theory categories.
Topology And Geometric Group Theory
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Author : Michael W. Davis
language : en
Publisher: Springer
Release Date : 2016-09-14
Topology And Geometric Group Theory written by Michael W. Davis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-14 with Mathematics categories.
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 2008
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Dissertations, Academic categories.
Whitehead Groups Of Finite Groups
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Author : Robert Oliver
language : en
Publisher: Cambridge University Press
Release Date : 1988-02-25
Whitehead Groups Of Finite Groups written by Robert Oliver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-02-25 with Mathematics categories.
This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area.
Braid Groups
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Author : Christian Kassel
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-28
Braid Groups written by Christian Kassel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-28 with Mathematics categories.
In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Algebraic K Theory Of Crystallographic Groups
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Author : Daniel Scott Farley
language : en
Publisher: Springer
Release Date : 2014-08-27
Algebraic K Theory Of Crystallographic Groups written by Daniel Scott Farley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives a powerful method for computing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class of three-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifying spaces. Later chapters assemble the techniques that are needed to apply the isomorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphism conjecture, and a contribution to the growing literature in the field.
Cohomology Of Groups And Algebraic K Theory
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Author : Lizhen Ji
language : en
Publisher: International Press of Boston
Release Date : 2010
Cohomology Of Groups And Algebraic K Theory written by Lizhen Ji and has been published by International Press of Boston this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Cohomology operations categories.
Cohomology of Groups and Algebraic K-theory --
Braids Links And Mapping Class Groups Am 82 Volume 82
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Author : Joan S. Birman
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Braids Links And Mapping Class Groups Am 82 Volume 82 written by Joan S. Birman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.