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Additive invariants for knots, links and graphs in 3-manifolds
Journal article   Peer reviewed

Additive invariants for knots, links and graphs in 3-manifolds

Scott A Taylor and Maggy Tomova
Geometry & topology, Vol.22(6), pp.3235-3286
01/01/2018
DOI: 10.2140/gt.2018.22.3235
url
https://arxiv.org/pdf/1606.03408View
Open Access

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.
Mathematics Physical Sciences Science & Technology

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