Abstract
AbstractA homeomorphismfof a manifoldMis calledH1-transitive if there is a transitive lift of an iterate offto the universal Abelian cover$\tilde {M}$. Roughly speaking, this means thatfhas orbits which repeatedly and densely explore all elements ofH1(M). For a rel pseudo-Anosov map ϕ of a compact surfaceMwe show that the following are equivalent: (a) ϕ isH1-transitive, (b) the action of ϕ onH1(M) has spectral radius one and (c) the lifts of the invariant foliations of ϕ to$\tilde {M}$have dense leaves. The proof relies on a characterization of transitivity for twisted ℤd-extensions of a transitive subshift of finite type.
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