Prising apart geodesics by length in hyperbolic manifolds
Prising apart geodesics by length in hyperbolic 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
547-572
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
May 2015
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Anderson, James W.
(2015)
Prising apart geodesics by length in hyperbolic manifolds.
Mathematical Proceedings of the Cambridge Philosophical Society, 158 (3), .
(doi:10.1017/S0305004115000146).
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
Text
lengths author final version 2015.02.13.pdf
- Accepted Manuscript
More information
Submitted date: February 2012
Accepted/In Press date: February 2015
e-pub ahead of print date: 24 March 2015
Published date: May 2015
Keywords:
length, hyperbolic metric, simple curves, horowitz tuple
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 210789
URI: http://eprints.soton.ac.uk/id/eprint/210789
ISSN: 0305-0041
PURE UUID: f4dbe8a1-87a0-467f-803f-d6c4288abb9a
Catalogue record
Date deposited: 16 Feb 2012 10:35
Last modified: 15 Mar 2024 02:52
Export record
Altmetrics
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
