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Title:
Instanton Floer homology of (1,1)-knot
Speaker:
Abstract:
Instanton knot homology was first introduced by Floer and was revisited by Kronheimer and Mrowka via sutured instanton Floer homology. As the nature of instanton theory, the computation of instanton knot homology is in general very difficult. In this talk, we present the computations of some families of (1,1)-knots, including all torus knots. The computation involves two technical results, which are also interesting on their own. The first is to extract information about instanton theory from the Heegaard diagrams of 3-manifolds and knots. The second is to relate the Euler characteristics of sutured Instanton Floer homology and sutured Floer homology that was introduced by Juhász. This is a joint work with Fan Ye.
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