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H. Imori 3-17-2022

Title:  Instanton knot invariants with rational holonomy parameters and an application for torus knot groups
Abstract:  Several knot invariants from instantons provide powerful tools to study the topology of knots in terms of representations of knot groups. In this talk, we introduce a generalization of Daemi-Scaduto’s equivariant singular instanton Floer theory to rational holonomy parameters. As an application, it enables us to show that any SU(2)-representation of torus knot groups can be extended to the complement of any concordance from the torus knot to another knot. This result gives further evidence to a version of slice-ribbon conjecture to torus knots.

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