Do manifolds have little symmetry?

Volker Puppe

Published 2006-06-28Version 1

This note is surveying certain aspects (including recent results) of the following problem stated by F.Raymond and R.Schultz: ''It is generally felt that a manifold 'chosen at random' will have little symmetry. Can this intuitive notion be made more precise? Does there exist a closed simply connected manifold, on which no finite group acts effectively? (A weaker question, no involution?)''