An equivariant index formula in contact geometry

• Autores: Sean Fitzpatrick
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 2-3, 2009, págs. 375-394
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n3.a1
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• Resumen

  • 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 generalized coefficients $\mathcal{J}(E,X)$ defined in terms of a choice of contact form on $M$. We explain how the form $\mathcal{J}(E,X)$ is natural with respect to the contact structure, and give a formula for the equivariant index of $\dirac$ involving $\mathcal{J}(E,X)$. A key tool is the Chern character with compact support developed by Paradan-Vergne \cite{PV1,PV}.