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.
Download or read book The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups written by Daciberg Lima Goncalves and published by Springer Science & Business Media. This book was released on 2013-09-08 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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:
Download or read book Algebraic K theory of Crystallographic Groups written by Daniel Scott Farley and published by Springer. This book was released on 2014-08-27 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic K Theory written by Vasudevan Srinivas and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic K theory And Its Applications Proceedings Of The School written by Hyman Bass and published by World Scientific. This book was released on 1999-03-12 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Download or read book Algebraic K Theory and Its Applications written by Jonathan Rosenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
Download or read book Algebraic K theory written by Wayne Raskind and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 350 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 the most up-to-date published account of Voevodsky's proof of the Milnor conjecture relating the Milnor K-theory of fields to Galois cohomology. This book offers a comprehensive source for cutting-edge research on the topic.
Download or read book Algebraic K Theory written by Richard G. Swan and published by Springer. This book was released on 2006-11-14 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."
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:
Download or read book Cohomology of Groups and Algebraic K theory written by Lizhen Ji and published by International Press of Boston. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Groups and Algebraic K-theory --
Download or read book Transformation Groups and Algebraic K Theory written by Wolfgang Lück and published by Springer. This book was released on 2006-11-14 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Download or read book Algebraic K Theory written by R. Keith Dennis and published by Springer. This book was released on 2006-11-15 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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:
Download or read book Algebraic K Theory written by Vasudevan Srinivas and published by Birkhäuser. This book was released on 1995-11-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.
Download or read book Algebraic K Theory and Algebraic Topology written by P.G. Goerss and published by Springer. This book was released on 1993-07-31 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991. This book is the volume of proceedings for this meeting. The papers that appear here are representative of most of the lectures that were given at the conference, and therefore present a "snapshot" of the state ofthe K-theoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the Lichtenbaum-Quillen complex of conjectures, fro~ both the algebraic and topological points of view. The papers in this volume deal with a range of topics, including motivic cohomology theories, cyclic homology, intersection homology, higher class field theory, and the former telescope conjecture. This meeting was jointly funded by grants from NATO and the National Science Foun dation in the United States. I would like to take this opportunity to thank these agencies for their support. I would also like to thank the other members of the organizing com mittee, namely Paul Goerss, Bruno Kahn and Chuck Weibel, for their help in making the conference successful. This was the second NATO Advanced Study Institute to be held in this venue; the first was in 1987. The success of both conferences owes much to the professionalism and helpfulness of the administration and staff of Chateau Lake Louise.
