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

Published 18 Feb 2014 in math.GT | (1402.4253v4)

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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Authors (1)

Jungsoo Kim

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