Quadrisecants and essential secants of knots: a survey

Date:

Time:

2021 08 09

15:30 (GMT+0)

Speaker:

Elizabeth Denne

Knots and representation theory

A quadrisecant line is one which intersects a curve in at least four points. In this survey talk, we review the history and current state of knowledge about quadrisecants. We give key ideas behind the proof that non-trivial knots must have an alternating quadrisecant line. This includes the idea of an essential secant, which captures something about the knottedness of a knot. If time allows, we show how these ideas can be applied to questions about the geometry of a knot (for example total curvature and ropelength).

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