Taut foliations, Dehn surgery, and Braid Positivity

Siddhi Krishna (Georgia Tech)

Monday 24th May 16:00-17:00 Online

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!


The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).


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