ChernSimons functional and the Homology Cobordism Group
ChernSimons functional and the Homology Cobordism Group

Aliakbar Daemi, SCGP
Fine Hall 314
The set of 3manifolds with the same homology as the 3dimensional sphere, modulo an equivalence relation called *homology cobordance*, forms a group.The additive structure of this group is given by taking connected sum. This group is called the *homology cobordism group *and plays a special role in low dimensional topology and knot theory. In this talk, I will explain how one can construct a family of invariants of the homology cobordism group by applying ideas from minmax theory in Floer theory. The relationship between these invariants and the Froyshov’s invariant will be discussed. I will also talk about some topological applications.