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2011 Tunnel complexes of $3$–manifolds
Yuya Koda
Algebr. Geom. Topol. 11(1): 417-447 (2011). DOI: 10.2140/agt.2011.11.417

Abstract

For each closed 3–manifold M and natural number t, we define a simplicial complex Tt(M), the t–tunnel complex, whose vertices are knots of tunnel number at most t. These complexes have a strong relation to disk complexes of handlebodies. We show that the complex Tt(M) is connected for M the 3–sphere or a lens space. Using this complex, we define an invariant, the t–tunnel complexity, for tunnel number t knots. These invariants are shown to have a strong relation to toroidal bridge numbers and the hyperbolic structures.

Citation

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Yuya Koda. "Tunnel complexes of $3$–manifolds." Algebr. Geom. Topol. 11 (1) 417 - 447, 2011. https://doi.org/10.2140/agt.2011.11.417

Information

Received: 25 April 2010; Revised: 18 September 2010; Accepted: 1 November 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1216.57004
MathSciNet: MR2783233
Digital Object Identifier: 10.2140/agt.2011.11.417

Subjects:
Primary: 57M25
Secondary: 57M15, 57M27

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 1 • 2011
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