Fan Ye, Harvard University - 2-Torsions in Singular Instanton Homology

Explore a conference talk on the study of 2-torsions in singular instanton homology for knots, presented by Fan Ye from Harvard University at the Gauge Theory and Low Dimensional Topology conference. Delve into Shumakovitch's conjecture regarding 2-torsions in unreduced Khovanov homology of nontrivial knots and the investigation inspired by Kronheimer-Mrowka's spectral sequence. Learn about the comparison of homology groups with complex coefficients and Z/2 coefficients for fibered knots, and the aim to prove the existence of 2-torsions in framed instanton homology of closed 3-manifolds obtained from S^3 by 1/2 surgery along genus 1 knots. Gain insights into this ongoing joint work with Deeparaj Bhat and Zhenkun Li, presented during the conference held at the University of Miami's Lakeside Village Pavilion in April 2023.