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تسجيل مستخدم جديدIsotopy of the Dehn twist on K3#K3 after a single stabilization
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Jianfeng Lin
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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 $S^{2}times S^{2}$). 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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