Are large distance Heegaard splittings generic?

DOI10.1515/CRELLE.2011.154zbMath1248.57012arXiv1002.4292OpenAlexW2964328938MaRDI QIDQ3166322

Martin Lustig, Yoav Moriah

Publication date: 11 October 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4292

zbMATH Keywords

3-manifoldscurve complexHeegard splittings

Mathematics Subject Classification ID

General low-dimensional topology (57M99)

Related Items (10)

Infinitely many hyperbolic 3-manifolds admitting distance-\(d\) and genus-\(g\) Heegaard splittings ⋮ Dehn filling and the geometry of unknotting tunnels ⋮ Small eigenvalues of random 3-manifolds ⋮ A random link via bridge position is hyperbolic ⋮ Bilateral self-amalgamation of a Heegaard splitting and Hempel distance ⋮ The closure of a random braid is a hyperbolic link ⋮ The compression body graph has infinite diameter ⋮ Exceptional and cosmetic surgeries on knots ⋮ Unstabilized ∂-stabilization of a fat Heegaard splitting ⋮ Finiteness of mapping class groups: locally large strongly irreducible Heegaard splittings

Cites Work

• Random walks on the mapping class group
• The measure of the limit set of the handlebody group
• Finite covers of random 3-manifolds
• High distance Heegaard splittings via fat train tracks
• Interval exchange transformations and measured foliations
• Geometry of the complex of curves. I: Hyperbolicity
• Horizontal Dehn surgery and genericity in the curve complex
• 3-manifolds as viewed from the curve complex

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