Geometric Topology: Localization, Periodicity and Galois Symmetry

Dennis P. Sullivan

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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. T...

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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. TOC:Algebraic Constructions.- Homotopy Theoretical Localization.- Completions in Homotopy Theory.- Spherical Fibrations.- Algebraic Geometry.- The Galois Group in Geometric Topology.- References. Galois Symmetry in Manifold Theory At the Primes (Reprint from Proc. 1970 Nice ICM).- Postscript (2004).