IJPAM: Volume 83, No. 1 (2013)

CLOSED GEODESIC LENGTHS IN HYPERBOLIC
LINK COMPLEMENTS IN $S^3$

Sreekrishna Palaparthi
Department of Mathematics
IIT Guwahati
PIN 781039, Guwahati, Assam, INDIA


Abstract. Adams and Reid produced an upper bound for the length of a shortest closed geodesic in a hyperbolic knot or link complement in closed 3-manifolds which do not admit any Riemannian metric of negative curvature. We demonstrate that the length of an $n^{th}$ shortest closed geodesic in such manifolds is also bounded above for $n>1$ and produce explicit upper bound on this length.

Received: June 27, 2012

AMS Subject Classification: 57M25

Key Words and Phrases: hyperbolic knots, hyperbolic links, geodesics, closed geodesics, length spectrum, lengths of geodesics

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DOI: 10.12732/ijpam.v83i1.5 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 1