Finite group actions on 4-manifolds with nonzero Euler characteristic

Ignasi Mundet i Riera

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arXiv · 1312.3149

Finite group actions on 4-manifolds with nonzero Euler characteristic

Ignasi Mundet i Riera

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Abstract

We prove that if $X$ is a compact, oriented, connected $4$-dimensional smooth manifold, possibly with boundary, satisfying $\chi(X)\neq 0$, then there exists an integer $C\geq 1$ such that any finite group $G$ acting smoothly and effectively on $X$ has an abelian subgroup $A$ satisfying $[G:A]\leq C$, $\chi(X^A)=\chi(X)$, and $A$ can be generated by at most $2$ elements. Furthermore, if $\chi(X)<0$ then $A$ is cyclic. This proves, for any such $X$, a conjecture of Ghys. We also prove an analogous result for manifolds of arbitrary dimension and non-vanishing Euler characteristic, but restricted to pseudofree actions.

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BibTeX RIS

Ignasi Mundet i Riera. 2013-12-11. Finite group actions on 4-manifolds with nonzero Euler characteristic. https://arxiv.org/abs/1312.3149

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