## Institute for Mathematical Sciences

## Preprint ims91-9

** E. Cawley**
* The Teichmuller Space of an Anosov Diffeomorphism of $T^2$.*

Abstract: In this paper we consider the space of smooth conjugacy classes of an Anosov diffeomorphism of the two-torus. The only
2-manifold that supports an Anosov diffeomorphism is the
2-torus, and Franks and Manning showed that every such
diffeomorphism is topologically conjugate to a linear example,
and furthermore, the eigenvalues at periodic points are a
complete smooth invariant. The question arises: what sets of
eigenvalues occur as the Anosov diffeomorphism ranges over a
topological conjugacy class? This question can be
reformulated: what pairs of cohomology classes (one determined
by the expanding eigenvalues, and one by the contracting
eigenvalues) occur as the diffeomorphism ranges over a
topological conjugacy class? The purpose of this paper is to
answer this question: all pairs of H\"{o}lder reduced
cohomology classes occur.

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