## Algebraic & Geometric Topology

### A lower bound on tunnel number degeneration

Trenton Schirmer

#### 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 $K$.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1279-1308.

Dates
Revised: 3 August 2015
Accepted: 7 August 2015
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895846

Digital Object Identifier
doi:10.2140/agt.2016.16.1279

Mathematical Reviews number (MathSciNet)
MR3523039

Zentralblatt MATH identifier
1350.57012

#### Citation

Schirmer, Trenton. A lower bound on tunnel number degeneration. Algebr. Geom. Topol. 16 (2016), no. 3, 1279--1308. doi:10.2140/agt.2016.16.1279. https://projecteuclid.org/euclid.agt/1511895846

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