2012/07/15 by Carrillo Rouse, Paulo, Rouse, Paulo Carrillo, Paulo Carrillo Rouse +4
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1207.3514
openalex publication_date 2012/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a cohomological formula for the index of a fully elliptic\npseudodifferential operator on a manifold with boundary. As in the classic case\nof Atiyah-Singer, we use an embedding into an euclidean space to express the\nindex as the integral of a cohomology class depending in this case on a\nnoncommutative symbol, the integral being over a C^\∞-manifold called the\nsingular normal bundle associated to the embedding. The formula is based on a\nK-theoretical Atiyah-Patodi-Singer theorem for manifolds with boundary that is\ndrawn from Connes' tangent groupoid approach.\n