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Article
Combinatorics of simple closed curves on the twice punctured torus
In the standard enumeration of homotopy classes of curves on a surface as words in a generating set for the fundamental group it is a very hard problem to discern those that are simple. In this paper we descri...
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Article
Martin boundaries of random walks on Fuchsian groups
Let Γ be a finitely generated non-elementary Fuchsian group, and let μ be a probability measure with finite support on Γ such that supp μ generates Γ as a semigroup. If Γ contains no parabolic elements we show...
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Article
Markov maps associated with fuchsian groups
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Article
Foliations of polynomial growth are hyperfinite
We define a class of equivalence relations with polynomial growth and show that such relations always support finite invariant measures and are hyperfinite. In particular, foliations of polynomial growth defin...
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Article
The Rohlin tower theorem and hyper-finiteness for actions of continuous groups
We prove the Rohlin tower theorem for free measure preserving actions of locally compact second countable solvable groups and almost connected amenable groups. This theorem was known for l.c.s.c. abelian group...