On Torelli groups and Dehn twists of smooth 4-manifolds

IF 0.9 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2025-02-04 DOI:10.1112/blms.70009

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 $\partial X ≅ S^{3}$ is trivial after taking connected sums with enough copies of $S^{2} \times S^{2}$ .

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光滑4流形的Torelli群和Dehn扭转

这个音符有两个相关但独立的部分。首先，我们证明了Gay在S 4的光滑映射类群$S^4$上的一个最新结果的推广。其次，我们给出了Saeki工作结果的另一种证明，即沿单连通闭合光滑4流形X $X$与∂X≠s3 $\partial X\cong S^3$的边界球的Dehn扭转在取足够的连通和后是平凡的s2 × s2的副本$S^2\times S^2$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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