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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/195522
Which finite groups act smoothly on a given 4-manifold?
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We prove that for any closed smooth 4-manifold $X$ there exists a constant $C$ with the property that each finite subgroup $G<\operatorname{Diff}(X)$ has a subgroup $N$ which is abelian or nilpotent of class 2 , and which satisfies $[G: N] \leq C$. We give sufficient conditions on $X$ for $\operatorname{Diff}(X)$ to be Jordan, meaning that there exists a constant $C$ such that any finite subgroup $G<\operatorname{Diff}(X)$ has an abelian subgroup $A$ satisfying $[G: A] \leq C$. Some of these conditions are homotopical, such as having nonzero Euler characteristic or nonzero signature, others are geometric, such as the absence of embedded tori of arbitrarily large self-intersection arising as fixed point components of periodic diffeomorphisms. Relying on these results, we prove that: (1) the symplectomorphism group of any closed symplectic 4-manifold is Jordan, and (2) the automorphism group of any almost complex closed 4-manifold is Jordan.
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MUNDET I RIERA, Ignasi, SÁEZ CALVO, Carlos. Which finite groups act smoothly on a given 4-manifold?. _Transactions of the American Mathematical Society_. 2021. Vol. 375, núm. 2, pàgs. 1207-1260. [consulta: 21 de gener de 2026]. ISSN: 0002-9947. [Disponible a: https://hdl.handle.net/2445/195522]