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Elements of Homotopy Theory Sd George Whitehead

Author: George William Whitehead
Publisher:
ISBN:
Category : Homotopy theory
Languages : en
Pages :

Book Description

Elements of Homotopy Theory

Author: George W. Whitehead
Publisher: Springer Science & Business Media
ISBN: 1461263182
Category : Mathematics
Languages : en
Pages : 764

Book Description
As the title suggests, this book is concerned with the elementary portion of the subject of homotopy theory. It is assumed that the reader is familiar with the fundamental group and with singular homology theory, including the Universal Coefficient and Kiinneth Theorems. Some acquaintance with manifolds and Poincare duality is desirable, but not essential. Anyone who has taught a course in algebraic topology is familiar with the fact that a formidable amount of technical machinery must be introduced and mastered before the simplest applications can be made. This phenomenon is also observable in the more advanced parts of the subject. I have attempted to short-circuit it by making maximal use of elementary methods. This approach entails a leisurely exposition in which brevity and perhaps elegance are sacrificed in favor of concreteness and ease of application. It is my hope that this approach will make homotopy theory accessible to workers in a wide range of other subjects-subjects in which its impact is beginning to be felt. It is a consequence of this approach that the order of development is to a certain extent historical. Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.

Homotopy Theory. [By] George W. Whitehead. Compiled by Robert J. Aumann

Author: George William WHITEHEAD
Publisher:
ISBN:
Category :
Languages : en
Pages :

Book Description

Elements of Homotopy Theory

Author: George William Whitehead
Publisher:
ISBN: 9787506200912
Category : Homotopy theory
Languages : en
Pages : 744

Book Description

Homotopy Theory

Author: George William Whitehead
Publisher:
ISBN:
Category : Homotopy theory
Languages : en
Pages : 144

Book Description
This book consists of notes for a second-year graduate course in advanced topology given by Professor Whitehead at M.I.T. Presupposing a knowledge of the fundamental group and of algebraic topology as far as singular theory, it is designed to introduce the student to some of the more important concepts of homotopy theory. The book emphasizes (relative) CW-complexes, which the author believes to be the natural setting for obstruction theory, and follows the spirit of J.H.C. Whitehead's "combinatorial homotopy".

Recent Advances in Homotopy Theory

Author: George William Whitehead
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 92

Book Description

Homotopy Theory

Author: I. M. James
Publisher: Elsevier
ISBN: 1483184765
Category : Mathematics
Languages : en
Pages : 468

Book Description
Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.