The Dehn twist on a connected sum of two homology tori

Haochen Qiu

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arXiv · 2410.02461

The Dehn twist on a connected sum of two homology tori

Haochen Qiu

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Abstract

Kronheimer-Mrowka shows that the Dehn twist along a $3$-sphere in the neck of two $K3$ surfaces is not smoothly isotopic to the identity. Their result requires that the manifolds are simply connected and the signature of one of them is $16 \mod 32$. We generalize the Pin$(2)$-equivariant family Bauer-Furuta invariant to nonsimply connected manifolds, and construct a refinement of this invariant. We use it to show that, if $X_1,X_2$ are two homology tori such that the determinants $r_1,r_2$ of them are odd, then the Dehn twist along a $3$-sphere in the neck of $X_1\# X_2$ is not smoothly isotopic to the identity.

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BibTeX RIS

Haochen Qiu. 2024-10-03. The Dehn twist on a connected sum of two homology tori. https://arxiv.org/abs/2410.02461

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