Geometric Topology: Localization, Periodicity and Galois Symmetry
by Dennis Sullivan
Publisher: Springer 2005
Number of pages: 296
In 1970, Sullivan circulated a set of notes introducing localization and completion of topological spaces to homotopy theory, and other important concepts that have had a major influence on the development of topology. 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.
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This is the first treatment of the applications of the lower K- and L-groups to the topology of manifolds such as Euclidean spaces, via Whitehead torsion and the Wall finiteness and surgery obstructions. Only elementary constructions are used.
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The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology.
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The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. It also contains authoritative expositions of mapping tori and telescopes.
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