The number of strings on essential tangle decompositions of a knot can be unbounded

Nogueira, João Miguel

doi:10.2140/agt.2016.16.2535

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The number of strings on essential tangle decompositions of a knot can be unbounded

João Miguel Nogueira

Algebraic & Geometric Topology 16 (2016) 2535–2548

DOI: 10.2140/agt.2016.16.2535

Abstract

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 $n$ .

Keywords

essential tangle, essential tangle decomposition, meridional essential surface

Mathematical Subject Classification 2010

Primary: 57M25, 57N10

References

Publication

Received: 16 April 2014

Revised: 28 July 2015

Accepted: 29 September 2015

Published: 7 November 2016

Authors

João Miguel Nogueira
CMUC Department of Mathematics University of Coimbra Apartado 3008 EC Santa Cruz 3001-501 Coimbra Portugal

Volume 16, issue 5 (2016)