Abstract
AbstractWe compute the topological simple structure set of closed manifolds that occur as total spaces of flat bundles over lens spaces Sl/(ℤ/p) with fiber Tn for an odd prime p and l ≥ 3 provided that the induced ℤ/p‐action on π1(Tn) = ℤn is free outside the origin. To the best of our knowledge this is the first computation of the structure set of a topological manifold whose fundamental group is not obtained from torsionfree and finite groups using amalgamated and HNN‐extensions. We give a collection of classical surgery invariants such as splitting obstructions and ρ‐invariants that decide whether a simple homotopy equivalence from a closed topological manifold to M is homotopic to a homeomorphism. © 2020 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC
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