Geodesic
A lower bound on tunnel number degeneration
Schirmer, Trenton1
1Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA
Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1279-1308
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

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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.

DOI : 10.2140/agt.2016.16.1279
Classification : 57M25, 57N10
Keywords: tunnel number, knots, Heegaard splittings, connected sum

Schirmer, Trenton  1

1 Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA 
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Schirmer, Trenton. A lower bound on tunnel number degeneration. Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1279-1308. doi: 10.2140/agt.2016.16.1279

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