2022/08/26 by Masoud Khalkhali, Khalkhali, Masoud, Ilya L. Shapiro +1
Mathematics · #16E40 #16T05 #16T10 #18D05 #18D10 #18D15 #19D55 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2208.12607
openalex publication_date 2022/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is an introduction to Hopf cyclic cohomology with an emphasis on its most recent developments. We cover three major areas: the original definition of Hopf cyclic cohomology by Connes and Moscovici as an outgrowth of their study of transverse index theory on foliated manifolds, the introduction of Hopf cyclic cohomology with coefficients by Hajac-Khalkhali-Rangipour-Sommerhauser, and finally the latest episode on unifying the coefficients as well as extending the notion to more general settings beyond Hopf algebras. In particular, the last section discusses the relative Hopf cyclic theory that arises in the braided monoidal category settings.