McShane's Identity in Rank One Symmetric Spaces

Abstract

In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods unify most of the existing methods used in the existing literature for proving this class of identities.

27 pages

References in corpus (3)

• Cross Ratios and Identities for Higher Thurston Theory
• Generalized Markoff Maps and McShane's Identity
• Delambre-Gauss Formulas for Augmented, Right-Angled Hexagons in Hyperbolic 4-Space