Maps on infra-nilmanifolds
Kyung-Chang Lee · Pacific Journal of Mathematics · 1995
We show that Bieberbach's rigidity theorem for flat manifolds still holds true for any continuous maps on infra-nilmanifolds.Namely, every endomorphism of an almost crystallographic group is semi-conjugate to an affine endomorphism.Applying this result to Fixed-point theory, we obtain a criterion for the Lefschetz number and Nielsen number for a map on infra-nilmanifolds to be equal. Infra-nilmanifolds.Let G be a connected Lie group.Consider the semi-group Endo(G), the set of all endomorphisms of G, under the composition as operation.We form the semi-direct product G x Endo(G) and call it aff(G).With the binary operation