Toeplitz operators and the full asymptotic torsion forms

Article Mathematics

The asymptotics of the holomorphic analytic torsion forms

Martin Puchol

Summary: The purpose of this paper is to provide an asymptotic formula for the holomorphic analytic torsion forms of a fibration associated with a sequence of direct images of increasing powers of a line bundle on a bigger manifold. To deal with the increasing dimension of the direct images, the theory of Toeplitz operators is utilized. This work extends the results of Bimsut and Vasserot on the asymptotics of the holomorphic torsion to more general bundles.

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2023)

添加到收藏夹

Article Mathematics

Asymptotic equivariant real analytic torsions for compact locally symmetric spaces

Bingxiao Liu

Summary: This paper investigates the asymptotics of equivariant analytic torsions for a certain sequence of flat vector bundles over a compact locally symmetric space, utilizing the twisted trace formula and an explicit geometric formula for the twisted orbital integrals. The leading term of the asymptotic equivariant analytic torsion is shown to be given in terms of W-invariants with oscillating coefficients.

JOURNAL OF FUNCTIONAL ANALYSIS (2021)

添加到收藏夹

Article Mathematics