2005/10/21 by Yoshiaki Maeda, Maeda, Yoshiaki, Dominique Manchon +3 · 3 citations
Mathematics · #35S05 #58A10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #math.DG #math.FA #msc:35S05 #msc:58A10
paper · pdf · doi:10.48550/arxiv.math/0510454
minor corrections, references precised
openalex publication_date 2005/10/21 · arxiv created 2006/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) only holds for non-integer order symbol-valued forms and leads to an integration by parts formula and translation invariance for cut-off integrals on non-integer order classical symbols. The extended Wodzicki residue yields an even residue cycle on classical symbols and an odd cochain (the cosphere cochain) which measures an obstruction to Stokes' property of the cut-off integral on integer order symbol-valued forms.