Department of Mathematics

Geometry and Topology

  •  Siddhi Krishna, Columbia University
  •  Twist positivity, L-space knots, and concordance
  •  03/21/2023
  •  11:30 AM - 12:30 PM
  •  C304 Wells Hall
  •  Peter Kilgore Johnson (john8251@msu.edu)

In this talk, I’ll describe a braid word theoretic property, called “twist positivity”, which often puts strong restrictions on quantitative and geometric properties of a braid. I’ll describe some old and new results about twist positivity, as well as some new applications towards knot concordance. In particular, I’ll describe how using a suite of numerical knot invariants (including the braid index) in tandem allows one to prove that there is an infinite family of L-space knots (containing all positive torus knots and also an infinite family of hyperbolic knots) where every knot represents a distinct smooth concordance class. This confirms a prediction of the slice-ribbon conjecture. Everything I’ll discuss is joint work with Hugh Morton. I will assume little background about knot invariants for this talk – all are welcome!

 

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Michigan State University
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