Algebraic & Geometric Topology

A lower bound on tunnel number degeneration

Trenton Schirmer

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

Permanent link to this document
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

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57N10: Topology of general 3-manifolds [See also 57Mxx]

Keywords
tunnel number knots Heegaard splittings connected sum

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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