Toeplitz Operators on Contact Manifolds and Equivariant K-homology

2026/03/24 by Alexander Gorokhovsky, Erik van Erp · 1 voice
Mathematics · #math.KT #math.FA #math.OA

paper · pdf

arxiv published 2026/03/24 · arxiv updated 2026/04/16

Abstract

We present an equivariant generalization of Boutet de Monvel's index theorem for Toeplitz operators on contact manifolds. We prove that the Dirac operator and the Szegö projection determine the same class in equivariant K-homology, generalizing a theorem of Baum-Douglas-Taylor. We do not assume that the contact manifold is the boundary of a strictly pseudoconvex domain. The proof proceeds by a deformation linking the principal symbols of the classical and Heisenberg pseudodifferential calculi. 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.

Citations

• The Heisenberg Calculus, Index Theory and Cyclic (Co)homology
• K-homology and index theory on contact manifolds
• Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds
• The Index of Elliptic Operators: IV
• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS

Discussions

• Alexander Gorokhovsky, Erik van Erp: Toeplitz Operators on Contact Manifolds and Equivariant K-homology https://arxiv.org/abs/2603.23191 https://arxiv.org/pdf/2603.23191 https://arxiv.org/html/2603.23 [bsky, 0 points, 0 comments]

Related

• K-homology and index theory on contact manifolds
• The Heisenberg Calculus, Index Theory and Cyclic (Co)homology
• K-homology and Fredholm operators I: Dirac Operators
• Index theory of hypoelliptic operators on Carnot manifolds
• Equivariant Poincaré-Hopf theorem