Geometry & Topology

Additive invariants for knots, links and graphs in $3$–manifolds

Scott A Taylor and Maggy Tomova

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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.

Article information

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

thin position bridge number tunnel number


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.

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