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

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Hegenbarth F., PAMUK M., Repovs D.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.12, no.3, pp.1107-1121, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1007/s00009-014-0456-4
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1107-1121
  • Keywords: s-Cobordism, 4-Manifold, cohomological dimension and Homotopy self-equivalence, TOPOLOGICAL 4-MANIFOLDS, FUNDAMENTAL GROUP, DUALITY
  • Middle East Technical University Affiliated: Yes

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 pi, such that cd pi <= 2.