Topological rigidity for non-aspherical manifolds

By M. Kreck, W. Lück. 2005

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The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f : N ! M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h: N ! M such that h and f induce up to conjugation the same maps on the fundamental groups. We call such manifolds Borel manifolds. We give partial answers to this questions for S k ◊ S d , for sphere bundles over aspherical closed manifolds of dimension 3 and for 3-manifolds with torsionfree fundamental groups. We show that this rigidity is inherited under connected sums in dimensions 5. We also classify manifolds of dimension 5 or 6 whose fundamental group is the one of a surface and whose second homotopy group is trivial.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/61f0bb0c6d655cb38e659b9b3b6509967e0bd4ff

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, background): “More information about topologically rigid (not necessarily aspherical) manifolds can be found in [36].”