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2016 A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical
Jungsoo Kim
Algebr. Geom. Topol. 16(3): 1427-1451 (2016). 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.

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Jungsoo Kim. "A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical." Algebr. Geom. Topol. 16 (3) 1427 - 1451, 2016. https://doi.org/10.2140/agt.2016.16.1427

Information

Received: 18 August 2014; Revised: 25 July 2015; Accepted: 19 September 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1362.57027
MathSciNet: MR3523045
Digital Object Identifier: 10.2140/agt.2016.16.1427

Subjects:
Primary: 57M50

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

Rights: Copyright © 2016 Mathematical Sciences Publishers

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