Abstract
Boutet de Monvel constructed an algebra of boundary value problems for pseudodifferential operators on a manifold with boundary. We define periodic cyclic cocycles on the algebra of symbols of Boutet de Monvel operators. Cocycles of this form enable one to interpret the index formula for elliptic pseudodifferential boundary value problems in the Boutet de Monvel calculus due to Fedosov as the Chern–Connes pairing with the classes in $$K$$ -theory defined by elliptic symbols. We also consider the equivariant case. Namely, we construct periodic cyclic cocycles on the crossed product of the symbol algebra by a group acting on this algebra by automorphisms. Such crossed products arise in index theory of nonlocal boundary value problems with shift operators. DOI 10.1134/S1061920822040021
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
