Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/195522
Title: | Which finite groups act smoothly on a given 4-manifold? |
Author: | Mundet i Riera, Ignasi Sáez Calvo, Carlos |
Keywords: | Transformacions (Matemàtica) Varietats (Matemàtica) Topologia de baixa dimensió Varietats simplèctiques Transformations (Mathematics) Manifolds (Mathematics) Low-dimensional topology Symplectic manifolds |
Issue Date: | 2-Dec-2021 |
Publisher: | American Mathematical Society (AMS) |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1090/tran/8518 |
It is part of: | Transactions of the American Mathematical Society, 2021, vol. 375, num. 2, p. 1207-1260 |
URI: | http://hdl.handle.net/2445/195522 |
Related resource: | https://doi.org/10.1090/tran/8518 |
ISSN: | 0002-9947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
718118.pdf | 596.64 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License