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

Kim, Jungsoo

doi:10.2140/agt.2016.16.1427

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

Jungsoo Kim

Algebraic & Geometric Topology 16 (2016) 1427–1451

DOI: 10.2140/agt.2016.16.1427

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 $2$ if $F$ is topologically minimal.

Keywords

$3$–manifold, Heegaard splitting, disk complex, topologically minimal surface

Mathematical Subject Classification 2010

Primary: 57M50

References

Publication

Received: 18 August 2014

Revised: 25 July 2015

Accepted: 19 September 2015

Published: 1 July 2016

Authors

Jungsoo Kim
BK21 PLUS SNU Mathematical Sciences Division Seoul National University 1 Gwanak-ro Gwanak-Gu Seoul 08826 South Korea

Volume 16, issue 3 (2016)