FINITE GROUPS ACTING ON HOMOLOGY MANIFOLDSMichael
نویسندگان
چکیده
To the memory of Olga Taussky-Todd
منابع مشابه
On finite simple and nonsolvable groups acting on homology 4-spheres
The only finite nonabelian simple group acting on a homology 3-sphere necessarily non-freely is the dodecahedral group A5 ∼= PSL(2, 5) (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group A∗5 ∼= SL(2, 5)). In the present paper we show that the only finite simple groups acting on a homology 4-sphere, and in particular on the 4-sphere, a...
متن کاملOn the Classification of Finite Groups Acting on Homology 3-spheres
In previous work we showed that the only finite nonabelian simple group acting by diffeomorphisms on a homology 3sphere is the alternating or dodecahedral group A5. Here we characterize finite nonsolvable groups that act on a homology 3-sphere preserving orientation. We find exactly the finite nonsolvable groups that act orthogonally on the 3-sphere, plus two families of groups for which we do ...
متن کاملAlmost simple groups with Socle $G_2(q)$ acting on finite linear spaces
After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.
متن کاملA characterisation of S3 among homology spheres
We prove that an integral homology 3–sphere is S3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S3 . As an application we show that an irreducible integral homology sphere which is not S3 is the cyclic branched cover of odd prime order of at most four knots in S3 . A result on the structure of finite groups of odd order acting on integral ho...
متن کاملInvariant Symmetries of Unimodal Function Singularities
We classify finite order symmetries g of the 14 exceptional unimodal function singularities f in 3 variables, which satisfy a so-called splitting condition. This means that the rank 2 positive subspace in the vanishing homology of f should not be contained in one eigenspace of g⋆. We also obtain a description of the hyperbolic complex reflection groups appearing as equivariant monodromy groups ...
متن کامل