Topology And Groupoids

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Topology And Groupoids

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Author : Ronald Brown
language : en
Publisher: Booksurge Llc
Release Date : 2006

Topology And Groupoids written by Ronald Brown and has been published by Booksurge Llc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.

A Concise Course In Algebraic Topology

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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 1999-09

A Concise Course In Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09 with Mathematics categories.

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Introduction To Foliations And Lie Groupoids

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Author : I. Moerdijk
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-18

Introduction To Foliations And Lie Groupoids written by I. Moerdijk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-18 with Mathematics categories.

This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

An Introduction To Groups Groupoids And Their Representations

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Author : Alberto Ibort
language : en
Publisher: CRC Press
Release Date : 2019-10-28

An Introduction To Groups Groupoids And Their Representations written by Alberto Ibort and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-28 with Mathematics categories.

This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.

General Theory Of Lie Groupoids And Lie Algebroids

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Author : Kirill C. H. Mackenzie
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-09

General Theory Of Lie Groupoids And Lie Algebroids written by Kirill C. H. Mackenzie and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-09 with Mathematics categories.

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.

Equivariant Topology And Derived Algebra

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Author : Scott Balchin
language : en
Publisher: Cambridge University Press
Release Date : 2022

Equivariant Topology And Derived Algebra written by Scott Balchin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematics categories.

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

Combinatorial Group Theory

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Author : Daniel E. Cohen
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-17

Combinatorial Group Theory written by Daniel E. Cohen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-17 with Mathematics categories.

In this book the author aims to show the value of using topological methods in combinatorial group theory.

Elements Of Modern Topology

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Author : Ronald Brown
language : en
Publisher:
Release Date : 1968

Elements Of Modern Topology written by Ronald Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.

Homotopy Of Operads And Grothendieck Teichmuller Groups

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Author : Benoit Fresse
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-21

Homotopy Of Operads And Grothendieck Teichmuller Groups written by Benoit Fresse and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-21 with Mathematics categories.

The Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck–Teichmüller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.