2019/04/05 by Karsten Bohlen, Bohlen, Karsten, Jean-Marie Lescure +1
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1904.04069
openalex publication_date 2019/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator, canonically associated, via the so-called clutching map. To this end we adapt to our framework ideas coming from Baum-Douglas geometric K-homology and in particular we introduce a notion of geometric cycles, that can be categorized as a variant of the famous geometric K-homology groups, for the specific situation here. We also define a comparison map between this geometric K-homology theory and a relative K-theory group, directly associated to a fully elliptic pseudodifferential operator.