Department of Mathematics Calendar
Aliakbar Daemi, Simons Center for Geometry and Physics, Chern-Simons functional and the Homology Cobordism Group
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April 25 | 10:40 am - 11:30 am EDT
The set of 3-manifolds with the same homology as the 3-dimensional 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 min-max 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.