On the mapping class groups of 4-manifolds with 1-handles

Jianfeng Lin; Yi Xie; Boyu Zhang

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arXiv · 2501.11821

On the mapping class groups of 4-manifolds with 1-handles

Jianfeng Lin·Yi Xie·Boyu Zhang

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Abstract

We develop a framework that generalizes Budney-Gabai's $W_3$ invariant on $\pi_0\textrm{Diff}(S^1\times D^3,\partial)$ to 4-manifolds with 1-handles. As applications, we show that if $M=(S^1\times D^3)\natural \hat M$ where $\hat M$ either has the form $I\times Y$ or is a punctured aspherical manifold, then the center of the mapping class group of $M$ is of infinite rank.

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BibTeX RIS

Jianfeng Lin, Yi Xie, Boyu Zhang. 2025-01-21. On the mapping class groups of 4-manifolds with 1-handles. https://arxiv.org/abs/2501.11821

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