Induced $C^*$-complexes in metaplectic geometry
Algebraic Topology
2018-11-14 v3 Differential Geometry
Operator Algebras
Symplectic Geometry
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 the Kostant's symplectic spinor bundle. Defining a Hilbert -structure on this bundle for a suitable -algebra, we obtain an elliptic -complex in the sense of Mishchenko--Fomenko. Its cohomology groups appear to be finitely generated projective Hilbert -modules. The paper can serve as a guide for handling of differential complexes and PDEs on Hilbert bundles
Keywords
Cite
@article{arxiv.1711.09937,
title = {Induced $C^*$-complexes in metaplectic geometry},
author = {Svatopluk Krýsl},
journal= {arXiv preprint arXiv:1711.09937},
year = {2018}
}
Comments
37 pages, 3 figures, accepted in Communication in Mathematical Physics; an argumentation on the continuity of map T in the proof of Thm. 18 was corrected