Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. Euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogous statement remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting a smooth action on an acyclic 5-manifold are the alternating groups 𝔸₅ and 𝔸₆, and deduce from this a short list of finite groups, closely related to the finite subgroups of SO(5), which are the candidates for orientation-preserving actions on acyclic 5-manifolds.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
203-217
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- SISSA, Via Bonomea 256, 34136 Trieste, Italy
autor
- Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, 34100 Trieste, Italy
autor
- Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, 34100 Trieste, Italy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-3-1