A note on the complexity of h–cobordisms

Schwartz, Hannah R

doi:10.2140/agt.2020.20.3313

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A note on the complexity of $h$–cobordisms

Hannah R Schwartz

Algebraic & Geometric Topology 20 (2020) 3313–3327

DOI: 10.2140/agt.2020.20.3313

Abstract

We show that the number of double points of smoothly immersed $2$ –spheres representing certain homology classes of an oriented, smooth, closed, simply connected $4$ –manifold $X$ must increase with the complexity of corresponding $h$ –cobordisms from $X$ to $X$ . As an application, we give results restricting the minimal number of double points of immersed spheres in manifolds homeomorphic to rational surfaces.

Keywords

topology, manifold, smooth structures, spheres, $h$–cobordism

Mathematical Subject Classification 2010

Primary: 57Q20, 57Q99

References

Publication

Received: 1 December 2018

Revised: 19 January 2020

Accepted: 2 April 2020

Published: 29 December 2020

Authors

Hannah R Schwartz
Max Planck Institute of Mathematics Bonn Germany

Volume 20, issue 7 (2020)