Homotopy Invariant Algebraic Structures on Topological Spaces
Title | Homotopy Invariant Algebraic Structures on Topological Spaces PDF eBook |
Author | J. M. Boardman |
Publisher | Springer |
Pages | 268 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540377999 |
Homotopy Invariant Algebraic Structures
Title | Homotopy Invariant Algebraic Structures PDF eBook |
Author | Jean-Pierre Meyer |
Publisher | American Mathematical Soc. |
Pages | 392 |
Release | 1999 |
Genre | Mathematics |
ISBN | 082181057X |
This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.
Homotopy Invariant Algebraic Structures on Topological Spaces
Title | Homotopy Invariant Algebraic Structures on Topological Spaces PDF eBook |
Author | J. M. Boardman |
Publisher | |
Pages | 272 |
Release | 2014-01-15 |
Genre | |
ISBN | 9783662176238 |
Homotopy Invariant Algebraic Structures on Topological Spaces [by] J. M. Boardman [and] R. M. Vogt
Title | Homotopy Invariant Algebraic Structures on Topological Spaces [by] J. M. Boardman [and] R. M. Vogt PDF eBook |
Author | John M. Boardman |
Publisher | |
Pages | 257 |
Release | |
Genre | Homotopy theory |
ISBN |
Homotopy Theory of C*-Algebras
Title | Homotopy Theory of C*-Algebras PDF eBook |
Author | Paul Arne Østvær |
Publisher | Springer Science & Business Media |
Pages | 142 |
Release | 2010-09-08 |
Genre | Mathematics |
ISBN | 303460565X |
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.
Algebraic Structures Up to Homotopy
Title | Algebraic Structures Up to Homotopy PDF eBook |
Author | Ronald James Williams |
Publisher | |
Pages | 148 |
Release | 1975 |
Genre | Algebraic topology |
ISBN |
Algebraic Topology: A Structural Introduction
Title | Algebraic Topology: A Structural Introduction PDF eBook |
Author | Marco Grandis |
Publisher | World Scientific |
Pages | 372 |
Release | 2021-12-24 |
Genre | Mathematics |
ISBN | 9811248370 |
Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.