Geometry & Topology
- Geom. Topol.
- Volume 22, Number 6 (2018), 3235-3286.
Additive invariants for knots, links and graphs in $3$–manifolds
We define two new families of invariants for (–manifold, graph) pairs which detect the unknot and are additive under connected sum of pairs and () 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 –sphere. We give applications to the tunnel number and higher-genus bridge number of connected sums of knots.
Geom. Topol., Volume 22, Number 6 (2018), 3235-3286.
Received: 16 July 2016
Revised: 6 October 2017
Accepted: 15 October 2017
First available in Project Euclid: 29 September 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Taylor, Scott A; Tomova, Maggy. Additive invariants for knots, links and graphs in $3$–manifolds. Geom. Topol. 22 (2018), no. 6, 3235--3286. doi:10.2140/gt.2018.22.3235. https://projecteuclid.org/euclid.gt/1538186737