Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds

Jean-Marie Lescure (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

In a earlier work of Claire Debord and the author, a notion of noncommutative tangent space isdefined for a conical pseudomanifold and the Poincaré duality in $K$-theory is proved between this space and the pseudomanifold. The present paper continues this work. We show that an appropriate and natural presentation of the notion of symbols on a manifold generalizes right away to conical pseudomanifolds and that it enables us to interpret the Poincaré duality in the singular setting as a principal symbol map.

Mots clés: Index theory; Noncommutative geometry; pseudomanifolds; Lie groupoids; bivariant K-theory; Index theory.

Domaines: Algèbres d'opérateurs [math.OA]

Jean-Marie Lescure. Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds. J. K-theory, 2009, 4 (2), pp.263--297. ⟨hal-00092760v2⟩