On Torelli groups and Dehn twists of smooth 4-manifolds

Manuel Krannich; Alexander Kupers

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arXiv · 2105.08904

On Torelli groups and Dehn twists of smooth 4-manifolds

Manuel Krannich·Alexander Kupers

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Abstract

This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply-connected closed smooth $4$-manifold $X$ with $\partial X\cong S^3$ is trivial after taking connected sums with enough copies of $S^2\times S^2$.

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Manuel Krannich, Alexander Kupers. 2021-05-19. On Torelli groups and Dehn twists of smooth 4-manifolds. https://arxiv.org/abs/2105.08904

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