ALGEBRAIC AND GEOMETRIC TOPOLOGY, cilt.15, sa.2, ss.1031-1066, 2015 (SCI-Expanded)
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.