Tightness and computing distances in the curve complex
Abstract
We give explicit bounds on the intersection number between any curve on a tight multigeodesic and the two ending curves. We use this to construct all tight multigeodesics and so conclude that distances in the curve graph are computable. The algorithm applies to all surfaces. We recover the finiteness result of MasurMinsky for tight goedesics. The central argument makes no use of the geometric limit arguments seen in the recent work of MasurMinsky (2000) and of Bowditch (2003), and is enough to deduce a computable version of the acylindricity theorem of Bowditch.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2004
 arXiv:
 arXiv:math/0412078
 Bibcode:
 2004math.....12078S
 Keywords:

 Geometric Topology;
 Geometric Topology
 EPrint:
 11 pages, no figures. v3: Corrected typos, updated references