2025/08/08 by Alex Taylor, Taylor, Alex R.
Computer Science · Mathematics · #19K56 #35K05 #58J20 #58J28 #58J35 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2508.06029
openalex publication_date 2025/08/08 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
We derive a transgression formula for the renormalized Chern character of the Bismut superconnection in the context of end-periodic fiber bundles and families of end-periodic Clifford modules. The transgression is expressed in terms of the Fourier-Laplace transform of the Bismut superconnection using the renormalized supertrace of Mrowka-Ruberman-Saveliev. Consequently, we establish an index formula for families of Dirac operators on end-periodic manifolds. The index formula involves a new ``end-periodic eta form'' which generalizes both the Bismut-Cheeger eta form and the end-periodic eta invariant of Mrowka-Ruberman-Saveliev.