Taut foliations, Dehn surgery, and Braid Positivity

Siddhi Krishna (Georgia Tech)

Abstract: The L-space conjecture predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections, with a focus towards "braid positive knots" (i.e. the knots realized as the closure of positive braids). I'll also present some applications, including obstructions to braid positivity, and a new unknot detector. Finally I'll briefly sketch a strategy for building taut foliations in manifolds obtained by Dehn surgery along knots in the three sphere. No background in foliations or Floer homology theories will be assumed. All are welcome!