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A lower bound on tunnel number degeneration

Trenton Schirmer

Algebraic & Geometric Topology 16 (2016) 1279–1308
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.

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