Mod-2 instanton homology and Dehn surgery

Abstract: Kim Froyshov has introduced new homology cobordism invariants q2(Y), q3(Y) coming from the study of mod-2 instanton homology. q3, in particular, has some remarkable properties: if Y, Y' cobound a 4-manifold W, then |q3(Y) - q3(Y')| is bounded in terms of homological invariants of W. I will explain the origin of this bound, how it leads to a resolution of the surgery number question, and directions for further inquiry.

This talk is based on forthcoming joint work with Ali Daemi and Xingpei Liu.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

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