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

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	197-209
Número de páginas	13
Publicación	Geometriae Dedicata
Volumen	91
N.º	1
DOI	https://doi.org/10.1023/A:1016226616826
Estado	Published - 2002

Nota bibliográfica

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.

Financiación

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. 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.

Financiadores	Número del financiador
University of Kentucky Research Professorship program
National Science Foundation (NSF)	DMS-9797051
University of Kentucky

ASJC Scopus subject areas

Geometry and Topology

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10.1023/A:1016226616826

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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\textbackslash{} 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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doi = "10.1023/A:1016226616826",

language = "English",

volume = "91",

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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

UR - https://www.scopus.com/pages/publications/0141676291

UR - https://www.scopus.com/pages/publications/0141676291#tab=citedBy

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DO - 10.1023/A:1016226616826

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AN - SCOPUS:0141676291

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

Resumen

Nota bibliográfica

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ASJC Scopus subject areas

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