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http://hdl.handle.net/2445/195522
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DC Field | Value | Language |
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dc.contributor.author | Mundet i Riera, Ignasi | - |
dc.contributor.author | Sáez Calvo, Carlos | - |
dc.date.accessioned | 2023-03-17T10:26:05Z | - |
dc.date.available | 2023-03-17T10:26:05Z | - |
dc.date.issued | 2021-12-02 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | http://hdl.handle.net/2445/195522 | - |
dc.description.abstract | 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. | - |
dc.format.extent | 54 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | American Mathematical Society (AMS) | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1090/tran/8518 | - |
dc.relation.ispartof | Transactions of the American Mathematical Society, 2021, vol. 375, num. 2, p. 1207-1260 | - |
dc.relation.uri | https://doi.org/10.1090/tran/8518 | - |
dc.rights | cc-by-nc-nd (c) American Mathematical Society (AMS), 2021 | - |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Transformacions (Matemàtica) | - |
dc.subject.classification | Varietats (Matemàtica) | - |
dc.subject.classification | Topologia de baixa dimensió | - |
dc.subject.classification | Varietats simplèctiques | - |
dc.subject.other | Transformations (Mathematics) | - |
dc.subject.other | Manifolds (Mathematics) | - |
dc.subject.other | Low-dimensional topology | - |
dc.subject.other | Symplectic manifolds | - |
dc.title | Which finite groups act smoothly on a given 4-manifold? | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 718118 | - |
dc.date.updated | 2023-03-17T10:26:05Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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718118.pdf | 596.64 kB | Adobe PDF | View/Open |
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