2020/09/19 by Aliakbar Daemi
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Topological and Geometric Data Analysis
paper · doi:10.1215/00127094-2020-0017
For each integral homology sphere Y , we construct a function Γ Y on the set of integers. We establish that Γ Y depends only on the homology cobordism class of Y and that it recovers the Frøyshov invariant. We state a relation between Γ Y and Fintushel and Stern’s R -invariant. We show that the value of Γ Y at each integer is related to the critical values of the Chern–Simons functional, and we give some topological applications of Γ Y . In particular, we show that if Γ Y is trivial, then there is no simply connected homology cobordism from Y to itself.