Connective Real $K$-Theory of Finite Groups
Title | Connective Real $K$-Theory of Finite Groups PDF eBook |
Author | Robert Ray Bruner |
Publisher | American Mathematical Soc. |
Pages | 328 |
Release | 2010 |
Genre | Mathematics |
ISBN | 0821851896 |
Focusing on the study of real connective $K$-theory including $ko^*(BG)$ as a ring and $ko_*(BG)$ as a module over it, the authors define equivariant versions of connective $KO$-theory and connective $K$-theory with reality, in the sense of Atiyah, which give well-behaved, Noetherian, uncompleted versions of the theory.
The Connective K-Theory of Finite Groups
Title | The Connective K-Theory of Finite Groups PDF eBook |
Author | Robert Ray Bruner |
Publisher | American Mathematical Soc. |
Pages | 144 |
Release | 2003 |
Genre | Mathematics |
ISBN | 0821833669 |
Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group
An Alpine Expedition through Algebraic Topology
Title | An Alpine Expedition through Algebraic Topology PDF eBook |
Author | Christian Ausoni |
Publisher | American Mathematical Soc. |
Pages | 314 |
Release | 2014-06-09 |
Genre | Mathematics |
ISBN | 0821891456 |
This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.
Geometry Of Spherical Space Form Groups, The (Second Edition)
Title | Geometry Of Spherical Space Form Groups, The (Second Edition) PDF eBook |
Author | Peter B Gilkey |
Publisher | World Scientific |
Pages | 508 |
Release | 2018-01-04 |
Genre | Mathematics |
ISBN | 9813220805 |
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.
Geometric and Topological Aspects of the Representation Theory of Finite Groups
Title | Geometric and Topological Aspects of the Representation Theory of Finite Groups PDF eBook |
Author | Jon F. Carlson |
Publisher | Springer |
Pages | 493 |
Release | 2018-10-04 |
Genre | Mathematics |
ISBN | 3319940333 |
These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Handbook of Homotopy Theory
Title | Handbook of Homotopy Theory PDF eBook |
Author | Haynes Miller |
Publisher | CRC Press |
Pages | 1043 |
Release | 2020-01-23 |
Genre | Mathematics |
ISBN | 1351251600 |
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
The $K$-book
Title | The $K$-book PDF eBook |
Author | Charles A. Weibel |
Publisher | American Mathematical Soc. |
Pages | 634 |
Release | 2013-06-13 |
Genre | Mathematics |
ISBN | 0821891324 |
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