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s-Cobordism Classification of 4-Manifolds Through the Group of Homotopy Self-equivalences

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Abstract

The aim of this paper is to give an s-cobordism classification of topological 4 manifolds in terms of the standard invariants using the group of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study the group of homotopy self-equivalences of 4-manifolds. Using this braid together with the modified surgery theory of Kreck, we give an s-cobordism classification for certain 4-manifolds with fundamental group π, such that cd π ≤ 2.

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Authors and Affiliations

  1. Department of Mathematics, University of Milano, Milano, Italy

    Friedrich Hegenbarth

  2. Department of Mathematics, Middle East Technical University, Ankara, 06531, Turkey

    Mehmetcik Pamuk

  3. Department of Mathematics and Physics, University of Ljubljana, Ljubljana, 1000, Slovenia

    Dušan Repovš

Authors
  1. Friedrich Hegenbarth
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  2. Mehmetcik Pamuk
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  3. Dušan Repovš
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Correspondence to Mehmetcik Pamuk.

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Hegenbarth, F., Pamuk, M. & Repovš, D. s-Cobordism Classification of 4-Manifolds Through the Group of Homotopy Self-equivalences. Mediterr. J. Math. 12, 1107–1121 (2015). https://doi.org/10.1007/s00009-014-0456-4

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  • DOI: https://doi.org/10.1007/s00009-014-0456-4

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