Author: D. R. AndersonPublisher:
ISBN:
Category :
Languages : en
Pages : 11
Book Description
The Simple Homotopy Theory of Controlled Spaces, an Announcement
Author: D. R. AndersonControlled Simple Homotopy Theory and Applications
Author: T. A. ChapmanPublisher: Springer
ISBN: 3540409734
Category : Mathematics
Languages : en
Pages : 97
Book Description
Geometry and Topology
Author: MccroryPublisher: CRC Press
ISBN: 9780824776213
Category : Mathematics
Languages : en
Pages : 370
Book Description
This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.
Geometry and Topology
Author: MccroryPublisher: CRC Press
ISBN: 1000110842
Category : Mathematics
Languages : en
Pages : 366
Book Description
This book discusses topics ranging from traditional areas of topology, such as knot theory and the topology of manifolds, to areas such as differential and algebraic geometry. It also discusses other topics such as three-manifolds, group actions, and algebraic varieties.
A Course in Simple-homotopy Theory
Author: Marshall M. CohenPublisher: Springer Science & Business Media
ISBN:
Category : Mathematics
Languages : en
Pages : 136
Book Description
Abstract Homotopy and Simple Homotopy Theory
Author: Klaus Heiner KampsPublisher: World Scientific
ISBN: 9789810216023
Category : Mathematics
Languages : en
Pages : 474
Book Description
"This book provides a thorough and well-written guide to abstract homotopy theory. It could well serve as a graduate text in this topic, or could be studied independently by someone with a background in basic algebra, topology, and category theory."
Lecture Notes in Pure and Applied Mathematics
Author: Categorical Homotopy Theory
Author: Emily RiehlPublisher: Cambridge University Press
ISBN: 1139952633
Category : Mathematics
Languages : en
Pages : 371
Book Description
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Simplicial Homotopy Theory
Author: Paul G. GoerssPublisher: Birkhäuser
ISBN: 3034887078
Category : Mathematics
Languages : en
Pages : 520
Book Description
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Cellular Spaces, Null Spaces and Homotopy Localization
Author: Emmanuel D. FarjounPublisher: Springer
ISBN: 3540484493
Category : Mathematics
Languages : en
Pages : 214
Book Description
In this monograph we give an exposition of some recent development in homotopy theory. It relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. It is applied to K-theory localizations, to Morava-theories, to Hopkins-Smith theory of types. The method of homotopy colimits is used heavily. It is written with an advanced graduate student in topology and research homotopy theorist in mind.