A lower bound on tunnel number degeneration

Schirmer, Trenton

doi:10.2140/agt.2016.16.1279

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A lower bound on tunnel number degeneration

Trenton Schirmer

Algebraic & Geometric Topology 16 (2016) 1279–1308

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 $t (K_{1} # K_{2}) \geq max {t (K_{1}), t (K_{2})}$ for any pair of knots $K_{1}, K_{2} \subset S^{3}$ , where $t (K)$ denotes the tunnel number of $K$ .

Keywords

tunnel number, knots, Heegaard splittings, connected sum

Mathematical Subject Classification 2010

Primary: 57M25, 57N10

References

Publication

Received: 3 December 2012

Revised: 3 August 2015

Accepted: 7 August 2015

Published: 1 July 2016

Authors

Trenton Schirmer
Department of Mathematics Oklahoma State University Stillwater, OK 74078 USA
http://www.trentschirmer.com

Volume 16, issue 3 (2016)