1999/06/29 by Ralf Meyer, Meyer, Ralf · 2 citations
Mathematics · #18G60 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:18G60
paper · pdf · doi:10.48550/arxiv.math/9906205
112 pages This is my thesis prepared under the supervision of Joachim Cuntz at the Universitaet Muenster
arxiv created 1999/06/29 · openalex publication_date 1999/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove excision in entire and periodic cyclic cohomology and construct a Chern-Connes character for Fredholm modules over a C*-algebra without summability restrictions, taking values in a variant of Connes's entire cyclic cohomology. Before these results can be obtained, we have to sort out some fundamental questions about the class of algebras on which to define entire cyclic cohomology. The right domain of definition for entire cyclic cohomology is the category of complete bornological algebras. For these algebras, we define a bivariant cohomology theory, called analytic cyclic cohomology, that contains Connes's entire cyclic cohomology as a special case. The definition of analytic cyclic cohomology is based on the Cuntz-Quillen approach to cyclic cohomology theories using tensor algebras and X-complexes. The appropriate completion of the tensor algebra that yields analytic cyclic cohomology can be understood using an appropriate notion of analytic nilpotence. In addition, we develop the elementary theory of analytic cyclic cohomology (smooth homotopy invariance, stability, Chern character in K-theory).