More Concise Algebraic Topology
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“530-46909_Ch00_5P.tex” — 8/19/2011 — 11:24 — page i chicago lectures in mathematics series Editors: Spencer J. Bloch, Peter Constantin, Benson Farb, Norman R. Lebovitz, Carlos Kenig, and J. P. May
Other Chicago Lectures in Mathematics titles available from the University of Chicago Press
Simplical Objects in Algebraic Topology, by J. Peter May (1967, 1993) Fields and Rings, Second Edition, by Irving Kaplansky (1969, 1972) Lie Algebras and Locally Compact Groups, by Irving Kaplansky (1971) Several Complex Variables, by Raghavan Narasimhan (1971) Torsion-Free Modules, by Eben Matlis (1973) Stable Homotopy and Generalised Homology, by J. F. Adams (1974) Rings with Involution, by I.N. Herstein (1976) Theory of Unitary Group Representation, by George V. Mackey (1976) Commutative Semigroup Rings, by Robert Gilmer (1984) Infinite-Dimensional Optimization and Convexity, by Ivar Ekeland and Thomas Turnbull (1983) Navier-Stokes Equations, by Peter Constantin and Ciprian Foias (1988) Essential Results of Functional Analysis, by Robert J. Zimmer (1990) Fuchsian Groups, by Svetlana Katok (1992) Unstable Modules over the Steenrod Algebra and Sullivan’s Fixed Point Set Conjecture, by Lionel Schwartz (1994) Topological Classification of Stratified Spaces, by Shmuel Weinberger (1994) Lectures on Exceptional Lie Groups, by J. F. Adams (1996) Geometry of Nonpositively Curved Manifolds, by Patrick B. Eberlein (1996) Dimension Theory in Dynamical Systems: Contemporary Views and Applications, by Yakov B. Pesin (1997) Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto Calderon´ , edited by Michael Christ, Carlos Kenig, and Cora Sadosky (1999) A Concise Course in Algebraic Topology, by J. P. May (1999) Topics in Geometric Group Theory, by Pierre de la Harpe (2000) Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, by Robert Bryant, Phillip Griffiths, and Daniel Grossman (2003) Ratner’s Theorems on Unipotent Flows, by Dave Witte Morris (2005) Geometry, Rigidity, and Group Actions, edited by Benson Farb and David Fisher (2011) Groups of Circle Diffeomorphisms, by Andrés Navas (2011)
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“530-46909_Ch00_5P.tex” — 8/19/2011 — 11:24 — page ii More Concise Algebraic Topology localization, completion, and model categories
J. P. May and K. Ponto
the university of chicago press • chicago and london −1 0 +1
“530-46909_Ch00_5P.tex” — 8/19/2011 — 11:24 — page iii J. P. May is professor of mathematics at the University of Chicago; he is author or coauthor of many papers and books, including Simplicial Objects in Algebraic Topology and A Concise Course in Algebraic Topology in this series.
K. Ponto is assistant professor of mathematics at the University of Kentucky; she is an algebraic topologist whose research has focused on topological fixed point theory.
The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2012 by The University of Chicago All rights reserved. Published 2012. Printed in the United States of America 201918171615141312 12345
ISBN-13: 978-0-226-51178-8 (cloth) ISBN-10: 0-226-51178-2 (cloth)
Library of Congress Cataloging-in-Publication Data
May, J. P. More concise algebraic topology : localization, completion, and model categories / J. P. May and K. Ponto. p. cm. — (Chicago lectures in mathematics series) ISBN-13: 978-0-226-51178-8 (hardcover : alk. paper) ISBN-10: 0-226-51178-2 (hardcover : alk. paper) 1. Algebraic topology. I. Ponto, Kate. II. Title. III. Series: Chicago lectures in mathematics. QA612.M388 2012 514'.2—dc22 2011012400