Georgia Institute of Technology College of Sciences

Instanton Floer homology, introduced by Floer in the 1980s, has become a power tool in the study of 3-dimensional topology. Its application has led to significant achievements, such as the proof of the Property P conjecture. While instanton Floer homology with complex coefficients is widely studied and conjectured to be isomorphic to the hat version of Heegaard Floer homology, its counterpart with integral coefficients is less understood. In this talk, we will explore the abundance of 2-torsion in instanton Floer homology with integral coefficients and demonstrate how this 2-torsion encodes intriguing topological information about relevant 3-manifolds and knots. This is a joint work with Fan Ye.