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.
"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