For each integral homology sphere , we construct a function on the set of integers. We establish that depends only on the homology cobordism class of and that it recovers the Frøyshov invariant. We state a relation between and Fintushel and Stern’s -invariant. We show that the value of at each integer is related to the critical values of the Chern–Simons functional, and we give some topological applications of . In particular, we show that if is trivial, then there is no simply connected homology cobordism from to itself.
Aliakbar Daemi. "Chern–Simons functional and the homology cobordism group." Duke Math. J. 169 (15) 2827 - 2886, 15 October 2020. https://doi.org/10.1215/00127094-2020-0017