Overview

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.

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From the reviews: <p> In 1970, Sullivan circulated a set of notes, the a ~MIT notesa (TM), introducing localization and completion of topological spaces to homotopy theory, and other important concepts a ] that have had a major influence on the development of topology. a ] The notes remain worth reading for the boldness of their ideas, the clear mastery of available structure they command, and the fresh picture they provide for geometric topology. The editor must be thanked for making the notes available to another generation of topologists. (John McCleary, Mathematical Reviews, Issue 2006 m)

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