Botany of transverse knots

Botany of transverse knots

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Doug LaFountain, Western Illinois University
Fine Hall 314

We study transverse representatives of an oriented topological knot type K in the tight contact 3-sphere, where the classical invariant of transverse isotopy introduced by Bennequin is the self-linking number. The botany problem for transverse knots, namely deciphering which transverse isotopy classes exist at a fixed self-linking value, has remained open in general, although for certain knot types a number of interesting botanical features have been shown to exist. In this talk we present partial solutions of the botany problem that hold for arbitrary knot types K.