Are large distance Heegaard splittings generic?
- 1 January 2012
- journal article
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2012 (670)
Abstract
27 pages 5 figuresInternational audienceIn a previous paper we introduced a notion of "genericity" for countable sets of curves in the curve complex of a surface S, based on the Lebesgue measure on the space of projective measured laminations in S. With this definition we prove that for each fixed g > 1 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of "genericity" is different and more intrinsic then the one given via random walksKeywords
All Related Versions
This publication has 10 references indexed in Scilit:
- Random walks on the mapping class groupDuke Mathematical Journal, 2011
- Horizontal Dehn surgery and genericity in the curve complexJournal of Topology, 2010
- High distance Heegaard splittings via fat train tracksTopology and its Applications, 2009
- Finite covers of random 3-manifoldsInventiones Mathematicae, 2006
- 3-Manifolds as viewed from the curve complexTopology, 2001
- Geometry of the complex of curves I: HyperbolicityInventiones Mathematicae, 1999
- The measure of the limit set of the handlebody groupTopology, 1990
- Measured foliations and handlebodiesErgodic Theory and Dynamical Systems, 1986
- Simplicial systems for interval exchange maps and measured foliationsErgodic Theory and Dynamical Systems, 1985
- Interval Exchange Transformations and Measured FoliationsAnnals of Mathematics, 1982