An equivariant index formula for elliptic actions on contact manifolds

2007/12/14 by Sean Fitzpatrick, Fitzpatrick, Sean · 1 citation
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0712.2431

openalex publication_date 2007/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M,E) one obtains two naturally associated objects: A G-transversally elliptic operator \dirac, and an equivariant differential form with generalised coefficients J(E,X) defined in terms of a choice of contact form on M. We explain how the form J(E,X) is natural with respect to the contact structure, and give a formula for the equivariant index of \dirac involving J(E,X). A key tool is the Chern character with compact support developed by Paradan-Vergne \citePV1,PV.

Cited by

• Note on a Cohomological Theory of Contact-Instanton and Invariants of Contact Structures

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