Geodesic
The number of strings on essential tangle decompositions of a knot can be unbounded
Nogueira, João Miguel1
1CMUC Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal
Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2535-2548
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We construct an infinite collection of knots with the property that any knot in this family has n–string essential tangle decompositions for arbitrarily high n.

DOI : 10.2140/agt.2016.16.2535
Classification : 57M25, 57N10
Keywords: essential tangle, essential tangle decomposition, meridional essential surface

Nogueira, João Miguel  1

1 CMUC Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal 
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Nogueira, João Miguel. The number of strings on essential tangle decompositions of a knot can be unbounded. Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2535-2548. doi: 10.2140/agt.2016.16.2535

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