Introduction to Homotopy Theory (Universitext) - Softcover

Arkowitz, Martin

Softcover

ISBN 10: 1441973281 ISBN 13: 9781441973283

Publisher: Springer, 2011

Synopsis

The unifying theme of this book is the Eckmann-Hilton duality theory, not to be found as the motif of any other text.  Since many topics occur in dual pairs, this provides motivation for the ideas and reduces the amount of repetitious material. This carefully written text moves at a gentle pace, even with fairly advanced material. In addition, there is a wealth of illustrations and exercises. The more difficult exercises are starred, and hints to them are given at the end of the book.
Key topics include:
*basic homotopy
*H-Spaces and Co-H-Spaces;
*cofibrations and fibrations;
*exact sequences;
*applications of exactness;
*homotopy pushouts and pullbacks and
 the classical theorems of homotopy theory;
*homotopy and homology decompositions;
*homotopy sets; and
*obstruction theory.
The book is written as a text for a second course in algebraic topology, for a topics seminar in homotopy theory, or for self instruction.

About this title

About the Author

Martin Arkowitz is currently a professor of mathematics at Dartmouth College. He received his Ph.D. in mathematics at Cornell University. His area of expertise is algebraic topology.

From the Back Cover

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows:

• Basic homotopy;
• H-spaces and co-H-spaces;
• Fibrations and cofibrations;
• Exact sequences of homotopy sets, actions, and coactions;
• Homotopy pushouts and pullbacks;
• Classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead;
• Homotopy sets;
• Homotopy and homology decompositions of spaces and maps; and
• Obstruction theory.

The underlying theme of the entire book is the Eckmann-Hilton duality theory. This approach provides a unifying motif, clarifies many concepts, and reduces the amount of repetitious material. The subject matter is treated carefully with attention to detail, motivation is given for many results, there are several illustrations, and there are a large number of exercises of varying degrees of difficulty.

It is assumed that the reader has had some exposure to the rudiments of homology theory and fundamental group theory; these topics are discussed in the appendices. The book can be used as a text for the second semester of an algebraic topology course. The intended audience of this book is advanced undergraduate or graduate students. The book could also be used by anyone with a little background in topology who wishes to learn some homotopy theory.

Edition details

• Publisher: Springer
• Publication date: 2011
• Language: English
• ISBN 10: 1441973281
• ISBN 13: 9781441973283
• Binding: Paperback
• Number of pages: 357