Fibrewise Homotopy Theory PDF Download

Author: Michael Charles Crabb
Publisher: Springer Science & Business Media
ISBN: 1447112652
Category : Mathematics
Languages : en
Pages : 344

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Book Description
Topology occupies a central position in modern mathematics, and the concept of the fibre bundle provides an appropriate framework for studying differential geometry. Fibrewise homotopy theory is a very large subject that has attracted a good deal of research in recent years. This book provides an overview of the subject as it stands at present.

Author: Yves Félix
Publisher: American Mathematical Soc.
ISBN: 0821849298
Category : Mathematics
Languages : en
Pages : 246

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Book Description
This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.

Author: Alejandro Adem
Publisher: American Mathematical Soc.
ISBN: 0821803050
Category : Mathematics
Languages : en
Pages : 250

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Book Description
This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.

Author: I.M. James
Publisher: Springer Science & Business Media
ISBN: 1461382831
Category : Mathematics
Languages : en
Pages : 253

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Book Description
Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group theory. This book is based on a course of 16 graduate lectures given at Oxford and elsewhere from time to time. In a course of that length one cannot discuss too many topics without being unduly superficial. However, this was never intended as a treatise on the subject but rather as a short introductory course which will, I hope, prove useful to specialists and non-specialists alike. The introduction contains a description of the contents. No algebraic or differen tial topology is involved, although I have borne in mind the needs of students of those branches of the subject. Exercises for the reader are scattered throughout the text, while suggestions for further reading are contained in the lists of references at the end of each chapter. In most cases these lists include the main sources I have drawn on, but this is not the type of book where it is practicable to give a reference for everything.

Author: I. M. James
Publisher: Cambridge University Press
ISBN: 9780521089258
Category : Mathematics
Languages : en
Pages : 0

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Book Description
The aim of this book is to promote a fibrewise perspective, particularly in topology, which is central to modern mathematics. Already this view is standard in the theory of fibre bundles and therefore in such subjects as global analysis. It has a role to play also in general and equivariant topology. There are strong links with equivariant topology, a topic which has latterly been subject to great research activity. It is to be hoped that this book will provide a solid and invigorating foundation for the increasing research interest in fibrewise topology

Author: Gijs Heuts
Publisher: Springer Nature
ISBN: 3031104471
Category : Mathematics
Languages : en
Pages : 622

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Book Description
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.

Author: I.M. James
Publisher: Elsevier
ISBN: 0080532985
Category : Mathematics
Languages : en
Pages : 1336

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Book Description
Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Author: Guido Mislin
Publisher: American Mathematical Soc.
ISBN: 0821802739
Category : Mathematics
Languages : en
Pages : 208

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Book Description
This volume presents a cross-section of new developments in algebraic topology. The main portion consists of survey articles suitable for advanced graduate students and professionals pursuing research in this area. A great variety of topics are covered, many of which are of interest to researchers working in other areas of mathematics. In addition, some of the articles cover topics in group theory and homological algebra.

Author: Mila Cenkl
Publisher: American Mathematical Soc.
ISBN: 0821802968
Category : Mathematics
Languages : en
Pages : 442

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Book Description
The June 1993 conference was organized to commemorate the 100th anniversary of the birth of Czech mathematician Edward Cech. The main topics of the conference were the most recent results in the stable and unstable homotopy theory. Among the topics in 22 refereed papers: on finiteness of subgroups of self-homotopy equivalences; the Chen groups of the pure braid group; Morava's change of rings theorem; the Boardman homomorphism; and a comparison criterion for certain loop spaces. No index. Annotation copyright by Book News, Inc., Portland, OR

Author: John F. Jardine
Publisher: Springer
ISBN: 1493923005
Category : Mathematics
Languages : en
Pages : 508

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Book Description
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory. Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences.