2023/03/28 by Nathan Couchet, Couchet, Nathan, Robert Yuncken +1
Mathematics · #35S05 #58H05 #58J40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 47G30 #secondary: 22A22
paper · pdf · doi:10.48550/arxiv.2303.15787
openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Originally, the noncommutative residue was studied in the 80's by Wodzicki in his thesis and Guillemin. In this article we give a definition of the Wodzicki residue, using the langage of r-fibered distributions in the context of filtered manifolds. We show that this groupoidal residue behaves like a trace on the algebra of pseudodifferential operators on filtered manifolds and coincides with the usual residue Wodzicki in the case where the manifold is trivially filtered. Moreover, in the context of Heisenberg calculus, we show that the groupoidal residue coincides with Ponge's definition for contact and codimension 1 foliation Heisenberg manifolds.