Abstract: Instanton Floer homology, introduced by Floer in the 1980s, has become a fundamental tool in the study of 3-dimensional topology. Significant achievements, such as the proof of the Property P conjecture, have been made possible through its application. In this talk, I will explore the divergence between instanton Floer homology with complex coefficients and integral coefficients. When using complex coefficients, instanton Floer homology aligns well with an axiomatic framework applicable to various versions of Floer theories. On the other hand, with integral coefficients, the torsion component of the Floer homology group presents a distinctive phenomenon unique to instanton theory, potentially leading to novel applications. This is a joint work with Fan Ye.
