arXiv subjects

Jean-Michel Bismut

Publications and source records attributed to Jean-Michel Bismut.

5 recordsLinked to original sources

arXiv2024

Anosov vector fields and Fried sections

The purpose of this paper is to prove that if $Y$ is a compact manifold, if $Z$ is an Anosov vector field on $Y$, and if $F$ is a flat vector bundle, there is a corresponding canonical nonzero section $τ_ν\left(i_{Z}\right)$ of the determinant line $ν=\det H\left(Y,F\right)$. In families, this section is $C^{1}$ with respect to the canonical smooth structure on $ν$. When $F$ is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on $ν$.

math.DG↗

arXiv2021

Coherent sheaves, superconnections, and RRG

Given a compact complex manifold, the purpose of this paper is to construct the Chern character for coherent sheaves with values in Bott-Chern cohomology, and to prove a corresponding Riemann-Roch-Grothendieck formula. Our paper is based on a fundamental construction of Block.

math.AG↗

arXiv2021

Geometric orbital integrals and the center of the enveloping algebra

The purpose of this paper is to extend the explicit geometric evaluation of semisimple orbital integrals for smooth kernels for the Casimir operator obtained by the first author to the case of kernels for arbitrary elements in the center of the enveloping algebra.

math.DG↗

arXiv2017

Eta invariants and the hypoelliptic Laplacian

The purpose of this paper is to give a new proof of results of Moscovici and Stanton on the orbital integrals associated with eta invariants on compact locally symmetric spaces. Moscovici and Stanton used methods of harmonic analysis on reductive groups. Here, we combine our approach to orbital integrals using the hypoelliptic Laplacian, with the introduction of a rotation on certain Clifford algebras. Probabilistic methods play an important role in establishing key estimates. In particular, we construct the proper It{ô} calculus associated with certain hypoelliptic diffusions.

math.DG↗

arXiv1995

Torus bundles and the group cohomology of GL(N,Z)

We prove the vanishing of a certain characteristic class of flat vector bundles when the structure groups of the bundles are contained in GL(N,Z). We do so by explicitly writing the characteristic class as an exact form on the base of the bundle.

dg-ga↗