The Bridgeman–Kahn identity for hyperbolic manifolds with cusped boundary

Nicholas G. Vlamis; Andrew Yarmola

doi:10.1007/s10711-017-0267-4

The Bridgeman–Kahn identity for hyperbolic manifolds with cusped boundary

Nicholas G. Vlamis
, Andrew Yarmola

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	81-97
Number of pages	17
Journal	Geometriae Dedicata
Volume	194
Issue number	1
DOIs	https://doi.org/10.1007/s10711-017-0267-4
State	Published - Jun 1 2018

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Geodesic boundary
Geometric identities
Hyperbolic manifold
Orthospectrum

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10.1007/s10711-017-0267-4

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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{\textquoteright}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.",

keywords = "Geodesic boundary, Geometric identities, Hyperbolic manifold, Orthospectrum",

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AU - Yarmola, Andrew

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N2 - 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.

AB - 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.

KW - Geodesic boundary

KW - Geometric identities

KW - Hyperbolic manifold

KW - Orthospectrum

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The Bridgeman–Kahn identity for hyperbolic manifolds with cusped boundary

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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