Closed geodesics in homology classes for convex co-compact hyperbolic manifolds

Jeffrey McGowan; Peter Perry

doi:10.1023/A:1016226616826

Closed geodesics in homology classes for convex co-compact hyperbolic manifolds

Jeffrey McGowan, Peter Perry

Mathematics

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

3 Scopus citations

Abstract

Let Γ be a convex co-compact, torsion-free, discrete group of isometries of real hyperbolic space Hⁿ⁺¹. We compute the asymptotics of the counting function for closed geodesics in homology classes for the quotient manifold X = Γ\ Hⁿ⁺¹, under the assumption that H ¹(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.

Original language	English
Pages (from-to)	197-209
Number of pages	13
Journal	Geometriae Dedicata
Volume	91
Issue number	1
DOIs	https://doi.org/10.1023/A:1016226616826
State	Published - 2002

Bibliographical note

Funding Information:
Jeffrey McGowan was supported in part by funds from the University of Kentucky Research Professorship program, and Peter Perry was supported in part by NSF grant DMS-9797051.

Funding Information:
We would like to thank Charles Epstein and Rafe Mazzeo for several helpful conversations. Peter Perry gratefully acknowledges the support of the University of Kentucky’s research professorship program and Jeffrey McGowan thanks the University of Kentucky for hospitality during part of the time this work was done.

Keywords

Closed geodesics
Hyperbolic manifolds
Selberg trace formula

ASJC Scopus subject areas

Geometry and Topology

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10.1023/A:1016226616826

Cite this

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title = "Closed geodesics in homology classes for convex co-compact hyperbolic manifolds",

abstract = "Let Γ be a convex co-compact, torsion-free, discrete group of isometries of real hyperbolic space Hn+1. We compute the asymptotics of the counting function for closed geodesics in homology classes for the quotient manifold X = Γ\ Hn+1, under the assumption that H 1(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.",

keywords = "Closed geodesics, Hyperbolic manifolds, Selberg trace formula",

author = "Jeffrey McGowan and Peter Perry",

note = "Funding Information: Jeffrey McGowan was supported in part by funds from the University of Kentucky Research Professorship program, and Peter Perry was supported in part by NSF grant DMS-9797051. Funding Information: We would like to thank Charles Epstein and Rafe Mazzeo for several helpful conversations. Peter Perry gratefully acknowledges the support of the University of Kentucky{\textquoteright}s research professorship program and Jeffrey McGowan thanks the University of Kentucky for hospitality during part of the time this work was done.",

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language = "English",

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AU - McGowan, Jeffrey

AU - Perry, Peter

N1 - Funding Information: Jeffrey McGowan was supported in part by funds from the University of Kentucky Research Professorship program, and Peter Perry was supported in part by NSF grant DMS-9797051. Funding Information: We would like to thank Charles Epstein and Rafe Mazzeo for several helpful conversations. Peter Perry gratefully acknowledges the support of the University of Kentucky’s research professorship program and Jeffrey McGowan thanks the University of Kentucky for hospitality during part of the time this work was done.

PY - 2002

Y1 - 2002

N2 - Let Γ be a convex co-compact, torsion-free, discrete group of isometries of real hyperbolic space Hn+1. We compute the asymptotics of the counting function for closed geodesics in homology classes for the quotient manifold X = Γ\ Hn+1, under the assumption that H 1(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.

AB - Let Γ be a convex co-compact, torsion-free, discrete group of isometries of real hyperbolic space Hn+1. We compute the asymptotics of the counting function for closed geodesics in homology classes for the quotient manifold X = Γ\ Hn+1, under the assumption that H 1(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.

KW - Closed geodesics

KW - Hyperbolic manifolds

KW - Selberg trace formula

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DO - 10.1023/A:1016226616826

M3 - Article

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SN - 0046-5755

VL - 91

SP - 197

EP - 209

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Closed geodesics in homology classes for convex co-compact hyperbolic manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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