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Systoles of hyperbolic 3-manifolds

Published online by Cambridge University Press:  01 January 2000

COLIN C. ADAMS  and
ALAN W. REID
COLIN C. ADAMS
Affiliation:
Department of Mathematics, Williams College, Williamstown MA 01267, U.S.A.
ALAN W. REID
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, U.S.A.
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Abstract

Let M be a complete hyperbolic n-manifold of finite volume. By a systole of M we mean a shortest closed geodesic in M. By the systole length of M we mean the length of a systole. We denote this by sl (M). In the case when M is closed, the systole length is simply twice the injectivity radius of M. In the presence of cusps, injectivity radius becomes arbitrarily small and it is for this reason we use the language of ‘systole length’.

In the context of hyperbolic surfaces of finite volume, much work has been done on systoles; we refer the reader to [2, 10–12] for some results. In dimension 3, little seems known about systoles. The main result in this paper is the following (see below for definitions):

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 1 , January 2000 , pp. 103 - 110
Copyright
The Cambridge Philosophical Society 2000

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