Basmajian-type inequalities for maximal representations
Copyright policy )Basmajian-type inequalities for maximal representations
For suitable metrics on the locally symmetric space associated to a maximal representation, we prove inequalities between the length of the boundary and the lengths of orthogeodesics that generalize the classical Basmajian's identity from Teichmueller theory. Any equality characterizes diagonal embeddings.
46 pages, 8 figures. Main addition: collar lemma-type statement for the locally symmetric space associated to a maximal representation. Further corrections/clarifications following referees' comments
generalized Teichmüller spaces, 53C15, 53C22, 30F60, Geometric Topology (math.GT), symplectic representations of fundamental group of surface, Group Theory (math.GR), Hermitian symmetric spaces, Lagrangian submanifolds, Ziegel domain, Mathematics - Geometric Topology, Basmajian identities, maximal representations, cross ratio, FOS: Mathematics, orthogeodesics, Shilov boundary, Teichmüller theory for Riemann surfaces, Mathematics - Group Theory, Differential geometry of symmetric spaces
generalized Teichmüller spaces, 53C15, 53C22, 30F60, Geometric Topology (math.GT), symplectic representations of fundamental group of surface, Group Theory (math.GR), Hermitian symmetric spaces, Lagrangian submanifolds, Ziegel domain, Mathematics - Geometric Topology, Basmajian identities, maximal representations, cross ratio, FOS: Mathematics, orthogeodesics, Shilov boundary, Teichmüller theory for Riemann surfaces, Mathematics - Group Theory, Differential geometry of symmetric spaces
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