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Induced C*-Complexes in Metaplectic Geometry

  • Svatopluk Krýsl
Article

Abstract

For a symplectic manifold admitting a metaplectic structure and for a Kuiper map, we construct a complex of differential operators acting on exterior differential forms with values in the dual of Kostant’s symplectic spinor bundle. Defining a Hilbert C*-structure on this bundle for a suitable C*-algebra, we obtain an elliptic C*-complex in the sense of Mishchenko–Fomenko. Its cohomology groups appear to be finitely generated projective Hilbert C*-modules. The paper can serve as a guide for handling differential complexes and PDEs on Hilbert bundles.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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