Filtered instanton Floer homology and the 3-dimensional homology cobordism group

Abstract: We introduce a family of real-valued homology cobordism invariants $r_s(Y)$ of oriented homology 3-spheres. The invariants $r_s(Y)$ are based on a quantitative construction of filtered instanton Floer homology. Using our invariants, we give several new constraints of the set of smooth boundings of homology 3-spheres. As one of the corollaries, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. As another corollary, we show that if the 1-surgery of a knot has negative Froyshov invariant, then the $1/n$-surgeries ($n>0$) of the knot are linearly independent in the homology cobordism group. This is joint work with Yuta Nozaki and Kouki Sato.

Mathematics

Audience: researchers in the topic

Regensburg low-dimensional geometry and topology seminar