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

1998/06/23 by Gabor Elek, Elek, Gabor
Mathematics · #22D40 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:22D40

paper · pdf · doi:10.48550/arxiv.math/9806128

7 pages LaTex

arxiv created 1998/06/23 · arxiv updated 2009/11/30

Abstract

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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