Tunnel complexes of 3-manifolds

Yuya Koda

doi:10.2140/agt.2011.11.417

Tunnel complexes of 3-manifolds

Yuya Koda

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

For each closed 3-manifold M and natural number t, we define a simplicial complex T_t(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 handle bodies. We show that the complex T_t(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.

Original language	English
Pages (from-to)	417-447
Number of pages	31
Journal	Algebraic and Geometric Topology
Volume	11
Issue number	1
DOIs	https://doi.org/10.2140/agt.2011.11.417
Publication status	Published - 2011

ASJC Scopus subject areas

Geometry and Topology

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