Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds

Details Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds

2006-09-12

arxiv.org/abs/math/0609328v2

J. K-theory 4, 2 (2009) 263-297

Mathematics

Operator Algebras

24 pages

Scientific paper

In a earlier work of Claire Debord and the author, a notion of noncommutative tangent space isdefined for a conical pseudomanifold and the Poincar\'e 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 Poincar\'e duality in the singular setting as a principal symbol map.

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