Gauge Theory and Topology Seminar: Surgery formulae in instanton theory

Gauge Theory and Topology Seminar, SEMINARS

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September 15, 2022 3:00 pm - 4:00 pm
Science Center Hall B
Address: 1 Oxford Street, Cambridge MA, 02139

Zhenkun Li - Stanford

Instanton homology was first introduced by Floer in 1980s. It has many important applications in the study of 3-manifolds and knots, especially in studying the SU(2) representations of fundamental groups. It is conjectured by Kronheimer and Mrowka that the framed instanton Floer homology of a 3-manifold is isomorphic to the hat version of Heegaard Floer homology, but not much is known beyond families of computational examples. In this talk, I will present some surgery formulae in instanton theory, which helps us understand the framed instanton Floer homology of Dehn surgeries on knots. These surgery formulae provide some important structural properties for instanton theory and enable us to compute the framed instanton Floer homology of many new families of 3-manifolds that come from Dehn surgeries and splicings. This is a join work with Fan Ye.