Low Dimensional Topology and Circle-valued Morse Functions

Explore a captivating conference talk on low-dimensional topology and circle-valued Morse functions presented by Steve Boyer from Université du Québec à Montréal. Delve into the intriguing world of Homeo_+(S^1) representations and their connection to the L-space conjecture. Discover how these representations can be utilized to verify the left-orderability of 3-manifold groups in various scenarios, including toroidal integer homology spheres, surgeries on knots, and cyclic branched covers of hyperbolic links. Examine the extent to which analogous results for the existence of taut foliations hold, as predicted by the L-space conjecture. Gain insights into the asymptotic behavior of foliations and flows on 3-manifolds and their relationship to fundamental group representations. This one-hour and eight-minute talk, part of the University of Miami's conference series, presents joint work with Cameron Gordon and Ying Hu, offering a deep dive into cutting-edge research in low-dimensional topology.