The Euler characteristic of discrete groups and Yuzvinskii's entropy addition formula

Details The Euler characteristic of discrete groups and Yuzvinskii's entropy addition formula The Euler characteristic of discrete groups and Yuzvinskii's entropy addition formula

1998-06-23

arxiv.org/abs/math/9806128v1

Mathematics

Dynamical Systems

7 pages LaTex

Scientific paper

The notion of topological entropy is originally defined for a single action. Later it was extended by Kieffer for arbitrary discrete amenable groups. Recently Friedland defined topological entropy for any discrete group actions amenable or not. Lind, Schmidt and Ward extended Yuzvinskii's addition formula from single action to abelian group actions. A result of Ward and Zhang suggests that such extension might be possible in the amenable case. In this paper we prove that the addition formula can not be extended for groups of finite type with nonzero Euler-characteristcs e.g. for free groups or surface groups.

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