Invariant Heegaard Surfaces in Manifolds with Involutions and the Heegaard Genus of Double Covers

Yo'av Rieck; J Hyam Rubinstein

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Invariant Heegaard Surfaces in Manifolds with Involutions and the Heegaard Genus of Double Covers

Yo'av Rieck·J Hyam Rubinstein

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Abstract

Let M be a 3-manifold admitting a strongly irreducible Heegaard surface S and f:M \to M an involution. We construct an invariant Heegaard surface for M of genus at most 8 g(S) - 7. As a consequence, given a (possibly branched) double cover π:M \to N we obtain the following bound on the Heegaard genus of N: g(N) \leq 4g(S) - 3. We also get a bound on the complexity of the branch set in terms of g(S). If we assume that M is non-Haken, by Casson and Gordon we may replace g(S) by g(M) in all the statements above.

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BibTeX RIS

Yo'av Rieck, J Hyam Rubinstein. 2010-01-04. Invariant Heegaard Surfaces in Manifolds with Involutions and the Heegaard Genus of Double Covers. https://arxiv.org/abs/math/0607145

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