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The Generalized Smale Conjecture for 3-manifolds with genus 2 one-sided Heegaard splittings

1997/12/07 by Darryl McCullough, J Rubinstein, McCullough, Darryl +2 · 2 citations
Mathematics · #57M99 (Primary) 57M50 (Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M50 #msc:57M99

paper · pdf · doi:10.48550/arxiv.math/9712233

23 pages

arxiv created 1997/12/07 · openalex publication_date 1997/12/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Generalized Smale Conjecture asserts that if M is a closed 3-manifold with constant positive curvature, then the inclusion of the group of isometries into the group of diffeomorphisms is a homotopy equivalence. For the 3-sphere, this was the classical Smale Conjecture proved by A. Hatcher. N. Ivanov proved the Generalized Smale Conjecture for the M which contain a 1-sided Klein bottle and such that no Seifert fibering is nonsingular on the complement of any vertical Klein bottle. We prove it in all remaining cases containing a one-sided Klein bottle, except for the lens space L(4,1).

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