Additive invariants for knots, links and graphs in 3-manifolds
Geometric Topology
2018-10-03 v2
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.
Cite
@article{arxiv.1606.03408,
title = {Additive invariants for knots, links and graphs in 3-manifolds},
author = {Scott A. Taylor and Maggy Tomova},
journal= {arXiv preprint arXiv:1606.03408},
year = {2018}
}
Comments
Accepted by G&T. Newest version includes some simplifications and an additional application to higher genus bridge number