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

Jianfeng Lin; Yi Xie; Boyu Zhang

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

Geometric Topology 2025-01-22 v1

Authors: Jianfeng Lin , Yi Xie , Boyu Zhang

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.

Keywords

mapping class group 4-manifold 1-handles Budney-Gabai invariant diffeomorphism group infinite rank

Cite

@article{arxiv.2501.11821,
  title  = {On the mapping class groups of 4-manifolds with 1-handles},
  author = {Jianfeng Lin and Yi Xie and Boyu Zhang},
  journal= {arXiv preprint arXiv:2501.11821},
  year   = {2025}
}

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43 pages

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

Abstract

Keywords

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