A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical

Jungsoo Kim

doi:10.2140/agt.2016.16.1427

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arXiv · 1402.4253

A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical

Jungsoo Kim

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Abstract

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological index of F is two if F is topologically minimal.

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BibTeX RIS

Jungsoo Kim. 2015-03-21. A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical. https://doi.org/10.2140/agt.2016.16.1427

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