The Bridgeman-Kahn identity for hyperbolic manifolds with cusped boundary

Abstract

In this note, we extend the Bridgeman-Kahn identity to all finite-volume orientable hyperbolic $n$-manifolds with totally geodesic boundary. In the compact case, Bridgeman and Kahn are able to express the manifold's volume as the sum of a function over only the orthospectrum. For manifolds with non-compact boundary, our extension adds terms corresponding to intrinsic invariants of boundary cusps.

18 pages, 7 figures

References in corpus (2)

• Chimneys, leopard spots, and the identities of Basmajian and Bridgeman
• Orthospectra of Geodesic Laminations and Dilogarithm Identities on Moduli Space