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Prising apart geodesics by length in hyperbolic 3-manifolds

Prising apart geodesics by length in hyperbolic 3-manifolds
Prising apart geodesics by length in hyperbolic 3-manifolds
In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyperbolic structures on the surface or 3-manifold completely determines the curve. For an orientable surface S of negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case on closed surfaces of genus two that we describe completely), while for hyperbolizable 3-manifolds M, we show that curves freely homotopic to simple curves on the boundary of M have this property
length, hyperbolic metric, simple curves, horowitz tuple
0305-0041
547-572
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98

Anderson, James W. (2015) Prising apart geodesics by length in hyperbolic 3-manifolds. Mathematical Proceedings of the Cambridge Philosophical Society, 158 (3), 547-572.

Record type: Article

Abstract

In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyperbolic structures on the surface or 3-manifold completely determines the curve. For an orientable surface S of negative Euler characteristic, we extend the known result that simple curves have this property to curves with self-intersection number one (with one exceptional case on closed surfaces of genus two that we describe completely), while for hyperbolizable 3-manifolds M, we show that curves freely homotopic to simple curves on the boundary of M have this property

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lengths author final version 2015.02.13.pdf - Accepted Manuscript
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More information

Submitted date: February 2012
Accepted/In Press date: February 2015
Published date: May 2015
Keywords: length, hyperbolic metric, simple curves, horowitz tuple
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 210789
URI: https://eprints.soton.ac.uk/id/eprint/210789
ISSN: 0305-0041
PURE UUID: f4dbe8a1-87a0-467f-803f-d6c4288abb9a
ORCID for James W. Anderson: ORCID iD orcid.org/0000-0002-7849-144X

Catalogue record

Date deposited: 16 Feb 2012 10:35
Last modified: 06 Jun 2018 13:03

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