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

· 2025 · math.GT · arXiv 2501.11821

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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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math.GT 1

years

2026 1

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CONDITIONAL 1

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Splitting spheres for $S^2$-links in $S^4$

math.GT · 2026-08-03 · conditional · novelty 8.0

Every smooth two-component split sphere link in S^4 admits infinitely many topologically non-isotopic splitting 3-spheres.

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  • Splitting spheres for $S^2$-links in $S^4$ math.GT · 2026-08-03 · conditional · none · ref 11 · internal anchor

    Every smooth two-component split sphere link in S^4 admits infinitely many topologically non-isotopic splitting 3-spheres.