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The L-space conjecture for 3-manifolds
Colloquium| Speaker: | Jacob Rasmussen, University of Illinois |
| Related Webpage: | https://rasmusj.web.illinois.edu/ |
| Location: | 1147 MSB |
| Start time: | Fri, Feb 20 2026, 4:10PM |
Description
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.