Volume 16, issue 3 (2016)

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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
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