English

Hypoelliptic Laplacian and twisted trace formula

Differential Geometry 2022-09-27 v2 Functional Analysis

Abstract

We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. In particular, we revisit the equivariant local index theorems and twisted L2L_{2}-torsions for locally symmetric spaces.

Keywords

Cite

@article{arxiv.1910.11382,
  title  = {Hypoelliptic Laplacian and twisted trace formula},
  author = {Bingxiao Liu},
  journal= {arXiv preprint arXiv:1910.11382},
  year   = {2022}
}

Comments

60 pages. This article will appear at Annales de l'Institut Fourier. Note that this updated version contains only the first part of the previous version, while the second part has been revised as a separate article published in Journal of Functional Analysis with the title Asymptotic equivariant real analytic torsions for compact locally symmetric spaces

R2 v1 2026-06-23T11:54:14.521Z