文档介绍：Geometric Topology
Localization, Periodicity, and Galois Symmetry
(The 1970 MIT notes)
by
Dennis Sullivan
Edited by Andrew Ranicki
ii
Dennis Sullivan
Department of Mathematics
The Graduate Center
City University of New York
365 5th Ave
New York, NY 10016-4309
USA
email: ******@
Mathematics Department
Stony Brook University
Stony Brook, NY 11794-3651
USA
email: ******@
Andrew Ranicki
School of Mathematics
University of Edinburgh
King’s Buildings
Mayfield Road
Edinburgh EH9 3JZ
Scotland, UK
email: a.******@
Contents
EDITOR’S PREFACE vii
PREFACE ix
1. ALGEBRAIC CONSTRUCTIONS 1
2. HOMOTOPY THEORETICAL
LOCALIZATION 31
3. COMPLETIONS IN HOMOTOPY THEORY 51
4. SPHERICAL FIBRATIONS 89
5. ALGEBRAIC GEOMETRY 113
6. THE GALOIS GROUP IN GEOMETRIC TOPOLOGY 187
REFERENCES 241
GALOIS SYMMETRY IN MANIFOLD THEORY AT
THE PRIMES
Reprint from Proc. 1970 Nice ICM 251
POSTSCRIPT (2004) 261
v
Editor’s Preface
The seminal ‘MIT notes’ of Dennis Sullivan were issued in June
1970 and were widely circulated at the time. The notes had a ma-
jor influence on the development of both algebraic and geometric
topology, pioneering
the localization pletion of spaces in homotopy theory,
including p-local, profinite and rational homotopy theory, lead-
ing to the solution of the Adams conjecture on the relationship
between vector bundles and spherical fibrations,
the formulation of the ‘Sullivan conjecture’ on the contractibility
of the space of maps from the classifying space of a finite group
to a finite dimensional plex,
the action of the Galois group over Q of the algebraic closure Qe of
Q on smooth manifold structures in profinite homotopy theory,
the K-theory orientation of P L manifolds and bundles.
Some of this material has been already published by Sullivan him-
self: in an article1 in the Proceedings of the 1970 Nice ICM, and
in the 1974 Annals of Mathematics papers ics of homotopy
th