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

Taylor, Scott¹ ; Tomova, Maggy²

¹ Department of Mathematics and Statistics, Colby College, Waterville, ME, United States
² Department of Mathematics, University of Iowa, Iowa City, IA, United States

Geometry & topology, Tome 22 (2018) no. 6, pp. 3235-3286.

Résumé

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 ($-\frac{1}{2}$) 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.

Détail

DOI : 10.2140/gt.2018.22.3235

Classification : 57M25, 57M27
Keywords: thin position, bridge number, tunnel number

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