The Goeritz group of a Heegaard splitting of genus two of a Seifert manifold whose base orbifold is sphere with three exceptional points of sufficiently complex coefficients

Nozomu Sekino

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arXiv · 2202.05064

The Goeritz group of a Heegaard splitting of genus two of a Seifert manifold whose base orbifold is sphere with three exceptional points of sufficiently complex coefficients

Nozomu Sekino

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Abstract

In this paper, we add examples to Goeritz groups, the mapping class groups of given Heegaard splittings of 3-manifolds. We focus on a Heegaard splitting of genus two of a Seifert manifold whose base orbifold is sphere with three exceptional points of sufficiently complex coefficients, where "sufficiently complex" means that every surgery coefficient p_{l} over q_{l} of each exceptional fiber (in a surgery description) satisfies that q_{l} is congruent to neither +1 or -1 modulo p_{l}.

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Nozomu Sekino. 2022-02-10. The Goeritz group of a Heegaard splitting of genus two of a Seifert manifold whose base orbifold is sphere with three exceptional points of sufficiently complex coefficients. https://arxiv.org/abs/2202.05064

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