Volume 11, issue 1 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Tunnel complexes of $3$–manifolds

Yuya Koda

Algebraic & Geometric Topology 11 (2011) 417–447
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.

Keywords
knot, unknotting tunnel, complex, toroidal bridge number
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M15, 57M27
References
Publication
Received: 25 April 2010
Revised: 18 September 2010
Accepted: 1 November 2010
Published: 25 January 2011
Authors
Yuya Koda
Mathematical Institute
Tohoku University
Sendai 980-8578
Japan
http://www.math.tohoku.ac.jp/~koda/index_e.html