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2016 A lower bound on tunnel number degeneration
Trenton Schirmer
Algebr. Geom. Topol. 16(3): 1279-1308 (2016). DOI: 10.2140/agt.2016.16.1279

Abstract

We prove a theorem that bounds the Heegaard genus from below under special kinds of toroidal amalgamations of 3–manifolds. As a consequence, we conclude that t(K1 # K2) max{t(K1),t(K2)} for any pair of knots K1,K2 S3, where t(K) denotes the tunnel number of K.

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Trenton Schirmer. "A lower bound on tunnel number degeneration." Algebr. Geom. Topol. 16 (3) 1279 - 1308, 2016. https://doi.org/10.2140/agt.2016.16.1279

Information

Received: 3 December 2012; Revised: 3 August 2015; Accepted: 7 August 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1350.57012
MathSciNet: MR3523039
Digital Object Identifier: 10.2140/agt.2016.16.1279

Subjects:
Primary: 57M25, 57N10

Rights: Copyright © 2016 Mathematical Sciences Publishers

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