Volume 15, issue 2 (2015)

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Nonlooseness of nonloose knots

Kenneth L Baker and Sinem Onaran

Algebraic & Geometric Topology 15 (2015) 1031–1066
Abstract

A Legendrian or transverse knot in an overtwisted contact $3$–manifold is nonloose if its complement is tight and loose if its complement is overtwisted. We define three measures of the extent of nonlooseness of a nonloose knot and show they are distinct.

Keywords
overtwisted contact structure, Legendrian knots, transverse knots, nonloose knots
Mathematical Subject Classification 2010
Primary: 53D10, 57M27