TY - JOUR
T1 - Tunnel complexes of 3-manifolds
AU - Koda, Yuya
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011
Y1 - 2011
N2 - 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 handle bodies. 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.
AB - 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 handle bodies. 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.
UR - http://www.scopus.com/inward/record.url?scp=79952968892&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952968892&partnerID=8YFLogxK
U2 - 10.2140/agt.2011.11.417
DO - 10.2140/agt.2011.11.417
M3 - Article
AN - SCOPUS:79952968892
VL - 11
SP - 417
EP - 447
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 1
ER -