An Alpine Anthology of Homotopy Theory
An Alpine Anthology of Homotopy Theory

Author: Dominique Arlettaz

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 228

ISBN-13: 082183696X

DOWNLOAD EBOOK

The second Arolla conference on algebraic topology brought together specialists covering a wide range of homotopy theory and $K$-theory. These proceedings reflect both the variety of talks given at the conference and the diversity of promising research directions in homotopy theory. The articles contained in this volume include significant contributions to classical unstable homotopy theory, model category theory, equivariant homotopy theory, and the homotopy theory of fusionsystems, as well as to $K$-theory of both local fields and $C*$-algebras.

Handbook of Homotopy Theory
Handbook of Homotopy Theory

Author: Haynes Miller

Publisher: CRC Press

Published: 2020-01-23

Total Pages: 1142

ISBN-13: 1351251600

DOWNLOAD EBOOK

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.

An Alpine Bouquet of Algebraic Topology
An Alpine Bouquet of Algebraic Topology

Author: Jérôme Scherer

Publisher: American Mathematical Soc.

Published: 2018-05-30

Total Pages: 322

ISBN-13: 147042911X

DOWNLOAD EBOOK

This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.

Homotopy Theory of C*-Algebras
Homotopy Theory of C*-Algebras

Author: Paul Arne Østvær

Publisher: Springer Science & Business Media

Published: 2010-09-08

Total Pages: 142

ISBN-13: 303460565X

DOWNLOAD EBOOK

Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.

Interactions between Homotopy Theory and Algebra
Interactions between Homotopy Theory and Algebra

Author: Luchezar L. Avramov

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 352

ISBN-13: 0821838148

DOWNLOAD EBOOK

This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.

Homotopy Theory: Tools and Applications
Homotopy Theory: Tools and Applications

Author: Daniel G. Davis

Publisher: American Mathematical Soc.

Published: 2019-05-30

Total Pages: 282

ISBN-13: 1470442442

DOWNLOAD EBOOK

This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.

Equivariant Topology and Derived Algebra
Equivariant Topology and Derived Algebra

Author: Scott Balchin

Publisher: Cambridge University Press

Published: 2021-11-18

Total Pages: 357

ISBN-13: 1108931944

DOWNLOAD EBOOK

A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

A Handbook of Model Categories
A Handbook of Model Categories

Author: Scott Balchin

Publisher: Springer Nature

Published: 2021-10-29

Total Pages: 326

ISBN-13: 3030750353

DOWNLOAD EBOOK

This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.

Fusion Systems in Algebra and Topology
Fusion Systems in Algebra and Topology

Author: Michael Aschbacher

Publisher: Cambridge University Press

Published: 2011-08-25

Total Pages: 329

ISBN-13: 1107601002

DOWNLOAD EBOOK

A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.