3 papers
math.DG2026
Generalized Morse Functions, Excision and Higher Torsions
Martin Puchol, Junrong Yan
Comparing invariants from both topological and geometric perspectives is a key focus in index theorem. This paper compares higher analytic and topological torsions and establishes…
math.DG2025
Weyl Law for Schrödinger Operators on Noncompact Manifolds, Heat Kernel, and Karamata-Hardy-Littlewood Theorem
Xianzhe Dai, Junrong Yan
Building on our earlier work on heat kernel asymptotics for Schrödinger-type operators on noncompact manifolds, we establish both the classical and semiclassical Weyl laws for Sch…
math.DG2025
A gluing formula for the -valued index of odd symmetric operators
Maxim Braverman, Ahmad Reza Haj Saeedi Sadegh, Junrong Yan
We investigate Dirac-type operator on involutive manifolds with boundary with symmetry, which forces the index of to vanish. We study the secondary -valued index of el…