Monday

The following question was asked by Atiyah in the early days of instanton Floer theory: Is there a Milnor fiber description of the Floer homology of the links of singularities? In the late 1990s, I proved a closed form formula for the instanton Floer homology of Brieskorn homology spheres, which could be viewed as an answer to Atiyah's question for the links of Brieskorn singularities. In this talk, we will revisit that formula in light of the progress in gauge theory of the past twenty years. We obtain several new formulas for the instanton Floer homology of Brieskorn homology spheres, including one exclusively in terms of the monodromy of the Milnor fiber. This is a joint project with Kyoung-Seog Lee and Anatoly Libgober.