Open Access
Translator Disclaimer
2017 Koszul complexes, Birkhoff normal form and the magnetic Dirac operator
Nikhil Savale
Anal. PDE 10(8): 1793-1844 (2017). DOI: 10.2140/apde.2017.10.1793

Abstract

We consider the semiclassical Dirac operator coupled to a magnetic potential on a large class of manifolds, including all metric contact manifolds. We prove a sharp Weyl law and a bound on its eta invariant. In the absence of a Fourier integral parametrix, the method relies on the use of almost analytic continuations combined with the Birkhoff normal form and local index theory.

Citation

Download Citation

Nikhil Savale. "Koszul complexes, Birkhoff normal form and the magnetic Dirac operator." Anal. PDE 10 (8) 1793 - 1844, 2017. https://doi.org/10.2140/apde.2017.10.1793

Information

Received: 1 October 2015; Revised: 19 May 2017; Accepted: 20 June 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1371.35182
MathSciNet: MR3694007
Digital Object Identifier: 10.2140/apde.2017.10.1793

Subjects:
Primary: 35P20 , 81Q20
Secondary: 58J28 , 58J40

Keywords: Dirac operator , eta invariant , Weyl law

Rights: Copyright © 2017 Mathematical Sciences Publishers

JOURNAL ARTICLE
52 PAGES


SHARE
Vol.10 • No. 8 • 2017
MSP
Back to Top