接触流形上的 Toeplitz 算子与等价 K-同伪
K理论与同调
2026-04-20 v2 泛函分析
算子代数
摘要
我们提出了接触流形上 Toeplitz 算子等价化 Boutet de Monvel 指数定理的推广。我们证明，Dirac 算子和 Szegö 投影在等价 同伪中决定相同的类，推广了 Baum-Douglas-Taylor 定理。我们不假设接触流形是严格 pseudoconvex 域的边界。该证明通过将经典和 Heisenberg 类伪微分算子的主符号进行变形链接。At the level of symbols, the projection defining the Dirac class deforms to the principal Heisenberg symbol of the Szegö projection. This deformation implies equality of the corresponding classes in K-homology. This, in turn, gives an equivariant generalization of Boutet de Monvel's index formula for Toeplitz operators.
引用
@article{arxiv.2603.23191,
title = {Toeplitz Operators on Contact Manifolds and Equivariant K-homology},
author = {Alexander Gorokhovsky and Erik van Erp},
journal= {arXiv preprint arXiv:2603.23191},
year = {2026}
}