Berge's distance 3 pairs of genus 2 Heegaard splittings

Author:

SCHARLEMANN MARTIN

Abstract

AbstractFollowing an example discovered by John Berge [2], we show that there is a 4-component link L ⊂ (S1 × S2)#(S1 × S2) so that, generically, the result of Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard splittings, and each of these Heegaard splittings is of Hempel distance 3.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference6 articles.

1. Genus two Heegaard splittings of orientable three-manifolds

2. 3-Manifolds as viewed from the curve complex

3. [3] Berge J. and Scharlemann M. Multiple genus 2 Heegaard splittings: a missed case, arXiv:0910.3921.

4. [2] Berge J. A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings, arXiv:0912.1315.

5. [1] Berge J. A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038.

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1. High distance Heegaard splittings via Dehn twists;Algebraic & Geometric Topology;2014-03-21

2. Hyperbolic volume and Heegaard distance;Communications in Analysis and Geometry;2014

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