Filtered instanton Floer homology and the homology cobordism group

Abstract: Note the time change!

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 a joint work with Yuta Nozaki and Masaki Taniguchi.

Mathematics

Audience: researchers in the topic

MIT Geometry and Topology Seminar

Series comments: Password is "topology".