
TL;DR
This paper investigates the asymptotic behavior of spectral flow for families of Dirac operators on spinor bundles, employing eta invariant variation and local index theory to derive uniform estimates as the parameter grows large.
Contribution
It introduces a novel approach combining eta invariant variation and local index theory to analyze spectral flow asymptotics for Dirac operators.
Findings
Established uniform eta invariant estimates for large parameters
Derived asymptotic formulas for spectral flow behavior
Applied heat kernel techniques for local index analysis
Abstract
In this paper we study the asymptotic behavior of the spectral flow of a one-parameter family of Dirac operators acting on the spinor bunldle twisted by a vector bundle of rank , with the parameter when gets sufficiently large. Our method uses the variation of eta invariant and local index theory technique. The key is a uniform estimate of the eta invariant which is established via local index theory technique and heat kernel estimate.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Numerical methods in inverse problems · Quantum chaos and dynamical systems
