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Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds

Published online by Cambridge University Press:  01 December 2008

Jean-Marie Lescure
Jean-Marie Lescure
Affiliation:
lescure@math.univ-bpclermont.frLaboratoire de Mathématiques UMR6620Université Blaise PascalCompexe Universtaire des Cézeaux63177 AubiéreFrance
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Abstract

In [7], a notion of noncommutative tangent space is associated with a conical pseudomanifold and Poincaré duality in K-theory is proved between this space and the pseudomanifold. The present paper continues this line of work. We show that an appropriate presentation of the notion of symbol on a manifold generalizes right away to conical pseudomanifolds and that it enables us to interpret Poincaré duality in the singular setting as a noncommutative symbol map.

Keywords

Manifolds with isolated conical singularitiesbivariant K-theorygroupoidspseudodifferential calculus
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 2 , October 2009 , pp. 263 - 297
Copyright
Copyright © ISOPP 2009

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