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The Dehn twist on a connected sum of two homology tori

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arxiv 2410.02461 v2 pith:6JPVY3LZ submitted 2024-10-03 math.GT

Haochen Qiu This is my paper · ORCID
classification math.GT
keywords connecteddehntwistalonghomologyidentityinvariantisotopic
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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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  1. The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory

    math.GT 2024-11 conditional novelty 7.0 of 10

    Boundary Dehn twists on indefinite symplectic fillings of negatively-oriented Seifert rational homology spheres have infinite order, so the monodromy of weighted-homogeneous surface singularities is infinite order exc...

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