Introduction to Homotopy Theory
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 homotop
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Universitext Series Editors: Sheldon Axler San Francisco State University Vincenzo Capasso Università degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus J. MacIntyre Queen Mary, University of London Kenneth Ribet University of California, Berkeley Claude Sabbah CNRS, École Polytechnique Endre Süli University of Oxford Wojbor A. Woyczynski Case Western Reserve University
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext. For further volumes: http://www.springer.com/series/223
Martin Arkowitz
Introduction to Homotopy Theory
Martin Arkowitz Department of Mathematics Dartmouth College Hanover, NH 03755-3551 USA [email protected]
ISSN 0172-5939 e-ISSN 2191-6675 ISBN 978- 1- 4419- 7328- 3 e-ISBN 978-1-4419-7329-0 DOI 10.1007/978-1-4419-7329-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011933473 Mathematics Subject Classification (2010): 55Q05, 55R05, 55S35, 55S45, 55U30
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To Eleanor, my bashert, and to Dylan, Jake, and Gregory Arkowitz
Preface
This book deals with homotopy theory, which is one of the main branches of algebraic topology. The ideas and methods of homotopy theory have pervaded many parts of topology as well as many parts of mathematics. A general approach in these areas has been to reduce a geometric, analytic, or topological problem to a homotopy problem, and to then attempt to solve the homotopy problem, usually by algebraic methods. Thus, in addition to being interesting and important in its own right, homotopy theory has been successfully applied to geometry, analysis, and other parts of topology. There are seve
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