The Bridgeman–Kahn identity for hyperbolic manifolds with cusped boundary

Nicholas G. Vlamis, Andrew Yarmola

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)81-97
Number of pages17
JournalGeometriae Dedicata
Volume194
Issue number1
DOIs
StatePublished - Jun 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Geodesic boundary
  • Geometric identities
  • Hyperbolic manifold
  • Orthospectrum

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