Filtered instanton Floer homology and the homology cobordism group

Masaki Taniguchi

We introduce a family of real-valued homology cobordisminvariants r_s(Y) of oriented homology 3-spheres. The invariants r_s(Y) arebased on a quantitative construction of filtered instanton Floer homology.Using our invariants r_s(Y), we give several new constraints of the set ofsmooth compact 4-manifolds bounded by homology 3-spheres. As one of thecorollaries, we give infinitely many homology 3-spheres which cannot boundany definite 4-manifold. As another corollary, we show that if the1-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.

http://scgp.stonybrook.edu/video_portal/video.php?id=4653

Simons- Workshop: Floer homology in low-dimensional topology