On Basmajian's identities, and other stories

preprint2015arXivOpen access

Abstract

We give a different perspective on the (by now) classic Basmajian identity, and point out some related results, both in the setting of hyperbolic manifolds, and in the polyhedral setting \emph{without} any group acting. In the new version we give more geometric and combinatorial applications of the main ideas.

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