Volume 22, issue 6 (2018)

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

Volume 23
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Additive invariants for knots, links and graphs in $3$–manifolds

Scott A Taylor and Maggy Tomova

Geometry & Topology 22 (2018) 3235–3286
Abstract

We define two new families of invariants for (3–manifold, graph) pairs which detect the unknot and are additive under connected sum of pairs and ( 1 2) additive under trivalent vertex sum of pairs. The first of these families is closely related to both bridge number and tunnel number. The second of these families is a variation and generalization of Gabai’s width for knots in the 3–sphere. We give applications to the tunnel number and higher-genus bridge number of connected sums of knots.

Keywords
thin position, bridge number, tunnel number
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 16 July 2016
Revised: 6 October 2017
Accepted: 15 October 2017
Published: 23 September 2018
Proposed: Rob Kirby
Seconded: David Gabai, Cameron Gordon
Authors
Scott A Taylor
Department of Mathematics and Statistics
Colby College
Waterville, ME
United States
Maggy Tomova
Department of Mathematics
University of Iowa
Iowa City, IA
United States