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Elliptic symbols, elliptic operators and Poincar\'e duality on conical pseudomanifolds

Jean-Marie Lescure
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Abstract

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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Jean-Marie Lescure. 2006-09-12. Elliptic symbols, elliptic operators and Poincar\'e duality on conical pseudomanifolds. https://arxiv.org/abs/math/0609328

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