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Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds

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Abstract

Let M 1 and M 2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism \({\phi : {\partial}M_1 \to {\partial}M_2}\). We analyze the relationship between the sets of low genus Heegaard splittings of M 1, M 2, and M, assuming the map \({\phi}\) is “sufficiently complicated”. This analysis yields counter-examples to the Stabilization Conjecture, a resolution of the higher genus analogue of a conjecture of Gordon, and a result about the uniqueness of expressions of Heegaard splittings as amalgamations.

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  1. Pitzer College, Claremont, USA

    David Bachman

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  1. David Bachman
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Bachman, D. Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds. Math. Ann. 355, 697–728 (2013). https://doi.org/10.1007/s00208-012-0802-4

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  • DOI: https://doi.org/10.1007/s00208-012-0802-4

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