Skip to main content Accessibility help
×
Home

Systoles of hyperbolic 3-manifolds

  • COLIN C. ADAMS (a1) and ALAN W. REID (a2)

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, 1012] for some results. In dimension 3, little seems known about systoles. The main result in this paper is the following (see below for definitions):

Copyright

Related content

Powered by UNSILO

Systoles of hyperbolic 3-manifolds

  • COLIN C. ADAMS (a1) and ALAN W. REID (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.