High distance Heegaard splittings via fat train tracks

2007/06/05 by Martin Lustig, Lustig, Martin, Yoav Moriah +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT

paper · pdf · doi:10.48550/arxiv.0706.0599

25 pages no figures. to appear in Proceedings of "Knots Groups and 3-manifolds" Marseilles France 2006

openalex publication_date 2007/06/05 · arxiv created 2008/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.

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