The Connective K-Theory of Finite Groups
The Connective K-Theory of Finite Groups

Author: Robert Ray Bruner

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 144

ISBN-13: 0821833669

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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

Connective Real $K$-Theory of Finite Groups
Connective Real $K$-Theory of Finite Groups

Author: Robert Ray Bruner

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 328

ISBN-13: 0821851896

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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
The Connective K-Theory of Finite Groups

Author: Robert Ray Bruner

Publisher:

Published: 2014-09-11

Total Pages: 144

ISBN-13: 9781470403836

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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

A Relationship Between Connective K-theory of Finite Groups and Number Theory
A Relationship Between Connective K-theory of Finite Groups and Number Theory

Author: Michael Keogh

Publisher:

Published: 2018

Total Pages: 130

ISBN-13:

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We study the relationship between Euler classes in connective K-theory of certain metacyclic groups and Eulerian periods living in algebraic number fields. The division of these Euler classes living in connective K-Theory map into a subgroup of the cyclotomic units in the algebraic number fields. With the use of algebraic number theory we further the computations in connective K-theory for certain cases.

Transformation Groups and Algebraic K-Theory
Transformation Groups and Algebraic K-Theory

Author: Wolfgang Lück

Publisher: Springer

Published: 2006-11-14

Total Pages: 455

ISBN-13: 3540468277

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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.

The $K$-book
The $K$-book

Author: Charles A. Weibel

Publisher: American Mathematical Soc.

Published: 2013-06-13

Total Pages: 634

ISBN-13: 0821891324

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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

Higher Algebraic K-Theory: An Overview
Higher Algebraic K-Theory: An Overview

Author: Emilio Lluis-Puebla

Publisher: Springer

Published: 2006-11-14

Total Pages: 172

ISBN-13: 3540466398

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This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.

An Alpine Expedition through Algebraic Topology
An Alpine Expedition through Algebraic Topology

Author: Christian Ausoni

Publisher: American Mathematical Soc.

Published: 2014-06-09

Total Pages: 314

ISBN-13: 0821891456

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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.

Kleinian Groups which Are Limits of Geometrically Finite Groups
Kleinian Groups which Are Limits of Geometrically Finite Groups

Author: Ken'ichi Ōshika

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 136

ISBN-13: 0821837729

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Ahlfors conjectured in 1964 that the limit set of every finitely generated Kleinian group either has Lebesgue measure $0$ or is the entire $S^2$. This title intends to prove that this conjecture is true for purely loxodromic Kleinian groups which are algebraic limits of geometrically finite groups.