Abstract:Abstract. This paper is devoted to study of transformations on metric spaces. It is done in an effort to produce qualitative version of quasi-isometries which takes into account the asymptotic behavior of the Gromov product in hyperbolic spaces. We characterize a quotient semigroup of such transformations on Teichmüller space by use of simplicial automorphisms of the complex of curves, and we will see that such transformation is recognized as a "coarsification" of isometries on Teichmüller space which is rigid… Show more
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