Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds

Abstract

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.

24 pages

References in corpus (1)

• Groupoids and an index theorem for conical pseudo-manifolds

Cited by in corpus (1)

• Groupoids and an index theorem for conical pseudo-manifolds