3:00–4:00 pm
Title: The \(L\)-space conjecture for 3-manifolds
Abstract:
The \(L\)-space conjecture of Boyer-Gordon-Watson and Juhasz relates three very different properties that a closed 3-manifold \(M\) can possess. One of these properties is algebraic: is \(\pi_1(M)\) left orderable? The second is geometric: does the \(M\) admit a coorientable taut foliation? The third is analytic: is the Heegaard Floer homology \(M\) as simple as it can be, given the size of \(H_1(M)\). If the conjecture is true, it would reveal the existence of a striking dichotomy for rational homology 3-spheres. In this talk, I'll explain what each of the three conditions appearing in the \(L\)-space conjecture mean, and then discuss efforts to prove and disprove it, and why we should care.