Non-linear similarity revisited, by Ian Hambleton and Erik K. Pedersen

An equivariant homeomorphism between two representations of a finite group is called a topological similarity, and if the representations are not isomorphic, a non-linear similarity. Topological similarity implies isomorphism for groups of odd order by work of Hsiang-Pardon and Madsen-Rothenberg. We give another proof of this theorem (Corollary B) using techniques from bounded algebraic K- and L-theory. Our methods also apply to representations of even order groups, with certain restrictions on the isotropy (Theorem A). We obtain a new necessary condition for the existence of non-linear similarities (Corollary C).


Ian Hambleton <ian@mpim-bonn.mpg.de>
Erik K. Pedersen <erik@mpim-bonn.mpg.de>