SOME RESULTS AND CONJECTURES ON FINITE GROUPS ACTING ON HOMOLOGY SPHERES

This is a note based on a talk given in the Workshop on geometry and topology of 3-manifolds, Novosibirsk, 22-26 August 2005. We consider the class of finite groups, which admit arbitrary, i.e. not necessarily free actions on integer and mod 2 homology spheres, with an emphasis on the 3- and 4-dimensional cases. We recall some classical results and present some recent progress as well as new results, open problems and the emerging conjectural picture of the situation.