Asymptotic morphisms on contact manifolds and index theory

Pradeep Nandika Alwis, Purdue University

Abstract

Let X be a compact oriented contact manifold. Associate to X there is a symplectic conic manifold $\Sigma$ formed from the oriented contact 1-form. Boutet de Monvel and Guillemin have constructed a quantized structure on X associated to the symplectic manifold $\Sigma$. Using this quantized structure we construct an asymptotic morphism from the algebra of continuous functions on $\Sigma$ to the algebra of compact operators. Asymptotic morphisms are the basic elements in E-theory, a bivariant homology theory, introduced by Connes and Higson. We relate our asymptotic morphism to the index of elliptic Toeplitz operators defined on X.

Degree

Ph.D.

Advisors

Kaminker, Purdue University.

Subject Area

Mathematics

COinS