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Manifolds with Poly-Surface Fundamental Groups

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Abstract.

We study closed topological 2n-dimensional manifolds M with poly-surface fundamental groups. We prove that if M is simple homotopy equivalent to the total space E of a Y-bundle over a closed aspherical surface, where Y is a closed aspherical n-manifold, then M is s-cobordant to E. This extends a well-known 4-dimensional result of Hillman in [14] to higher dimensions. Our proof is different from that of the quoted paper: we use Mayer-Vietoris techniques and the properties of the \({\Bbb L}\)-theory assembly maps for such bundles.

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Authors and Affiliations

  1. Università di Modena e di Reggio Emilia, Modena, Italy

    Alberto Cavicchioli & Fulvia Spaggiari

  2. Università di Milano, Italy

    Friedrich Hegenbarth

Authors
  1. Alberto Cavicchioli
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  2. Friedrich Hegenbarth
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  3. Fulvia Spaggiari
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Cavicchioli, A., Hegenbarth, F. & Spaggiari, F. Manifolds with Poly-Surface Fundamental Groups. Mh Math 148, 181–193 (2006). https://doi.org/10.1007/s00605-005-0349-5

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