2000/12/13 by Michael Weiss, Michael S. Weiss, Weiss, Michael S. +2 · 2 citations
Mathematics · #19JXX #57N37 #57R50 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:19JXX #msc:57N37 #msc:57R50
paper · pdf · doi:10.48550/arxiv.math/0012101
56 pages; survey paper; appears also in "Surveys on Surgery Theory: Volume 2" (eds. S.Cappell, A.Ranicki, J.Rosenberg), Princeton University Press, Princeton, New Jersey; January 2001
arxiv created 2000/12/13 · openalex publication_date 2000/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a survey paper on spaces of automorphisms of manifolds and spaces of manifolds in a fixed homotopy type. It describes the main theorems of traditional surgery theory, but also the main theorems of pseudoisotopy theory, alias concordance theory, Waldhausen style. It culminates in (an outline of) a synthesis of these two theories, producing algebraic models, valid in a stable range, for spaces of manifolds in a fixed homotopy type. This is inspired by earlier work of Burghelea-Lashof and Hatcher. The algebraic models are a mix of algebraic L-theory and algebraic K-theory.