2024/09/08 by Minh Lam Nguyen, Nguyen, Minh Lam
Computer Science · Mathematics · #57Kxx #57Mxx #57Rxx #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2409.04954
openalex publication_date 2024/09/08 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28
In this paper, we study a model for S1-equivariant monopole Floer homology for rational homology three-spheres via a homological device called S-complex. Using the Chern-Simons-Dirac functional, we define an R-filtration on the (equivariant) complex of monopole Floer homology HM. This R-filtration fits HM into a persistent homology theory, from which one can define a numerical quantity called the spectral invariant ρ. The spectral invariant ρ is tied with the geometry of the underlying manifold. The main result of the papers shows that ρ provides an obstruction to the existence of positive scalar curvature metric on a ribbon homology cobordism.