Ciprian Manolescu - Knot complements, local Floer homology, and sheaf quantization - IPAM at UCLA
Recorded 28 October 2026. Ciprian Manolescu of Stanford University presents "Knot complements, local Floer homology, and sheaf quantization" at IPAM's Contact Geometry, Cluster Algebras and Skein Theory Workshop.Abstract: A well-known theorem of Gordon and Luecke says that knots in the three-sphere are determined by their complements. Boileau asked whether the same is true for null-homotopic knots in three-manifolds. We present two solutions to his conjecture: one found in joint work with Ali Daemi, Tye Lidman, and Nick Rozenblyum, and another found by GPT-6 Astra. Both solutions involve studying SU(2)-character varieties with Yang-Mills gauge theory. The first approach is more conceptual, involving singularity theory and a sheaf quantization approach to the local Floer homology of Lagrangian branes. The sheaf is a real analogue of the vanishing cycle sheaves from complex geometry. As a byproduct of our theory, we construct G-Casson invariants and G-local Floer homology for 3-manifolds, for any reductive Lie group G.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-contact-geometry-cluster-algebras-and-skein-theory/ Receive SMS online on sms24.me
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