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Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes (K-Monographs in Mathematics)

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The seminal `MIT notes' of Dennis Sullivan were issued in June 1970 and were widely circulated at the time, but only privately. The notes had a major influence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including P-local, profinite and rational homotopy theory, the Galois action on smooth manifold structures in profinite homotopy theory, and the K-theory orientation of PL manifolds and bundles. This is the first time that this major work has actually been published, and made available to anyone interested in topology.

Author(s): Dennis P. Sullivan
Series: K-Monographs in Mathematics
Edition: 1
Publisher: Springer
Year: 2005

Language: English
Pages: 293

CONTENTS......Page 6
EDITOR’S PREFACE......Page 7
PREFACE......Page 9
1. ALGEBRAIC CONSTRUCTIONS......Page 14
2. HOMOTOPY THEORETICAL LOCALIZATION......Page 44
3. COMPLETIONS IN HOMOTOPY THEORY......Page 63
4. SPHERICAL FIBRATIONS......Page 101
5. ALGEBRAIC GEOMETRY......Page 124
6. THE GALOIS GROUP IN GEOMETRIC TOPOLOGY......Page 198
REFERENCES......Page 251
GALOIS SYMMETRY IN MANIFOLD THEORY AT THE PRIMES......Page 261
POSTSCRIPT (2004)......Page 270