Isotopy of the Dehn twist on K3#K3 after a single stabilization

林剑锋 清华大学丘成桐数学科学中心

Geometric Analysis and Geometric Topology mathscidoc:2205.15002

Geometry & Topology
Kronheimer-Mrowka recently proved that the Dehn twist along a 3-sphere in the neck of K3#K3 is not smoothly isotopic to the identity. This provides a new example of self-diffeomorphisms on 4-manifolds that are isotopic to the identity in the topological category but not smoothly so. (The first such examples were given by Ruberman.) In this paper, we use the Pin(2)-equivariant Bauer-Furuta invariant to show that this Dehn twist is not smoothly isotopic to the identity even after a single stabilization (connected summing with the identity map on S2×S2). This gives the first example of exotic phenomena on simply connected smooth 4-manifolds that do not disappear after a single stabilization.
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@inproceedings{林剑锋isotopy,
  title={Isotopy of the Dehn twist on K3#K3 after a single stabilization  },
  author={林剑锋},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517171440956804245},
  booktitle={Geometry & Topology},
}
林剑锋. Isotopy of the Dehn twist on K3#K3 after a single stabilization . In Geometry & Topology. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517171440956804245.
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