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A note on the complexity of $h$–cobordisms

Hannah R Schwartz

Algebraic & Geometric Topology 20 (2020) 3313–3327
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