Gauge Theory Seminar: "Filtered instanton Floer homology and the homology cobordism group I"

Abstract: Fintushel-Stern and Furuta developed orbifold gauge theory to prove that an infinite family of Brieskorn 3-spheres are linearly independent in the homology cobordism group. In this work, by translating their work into the words of filtered instanton Floer homology, we introduce a family {r_s} of real-valued homology cobordism invariants, which is parametrized by non-positive real numbers (with negative infinity). As an application of the invariants, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another application, we show that if the 1-surgery of a knot has negative Froyshov invariant, then all positive 1/n-surgeries of the knot are linearly independent in the homology cobordism group. In this talk, we mainly focus on such applications.

Host: Aliakbar Daemi