Hartogs phenomena for Hermitian vector bundles
The invariant differential operators on a manifold with a given parabolic structure come in two classes, standard and non-standard, and can be further subdivided into regular and singular ones. The standard regular operators come in repeated patterns, the Bernstein-Gelfand-Gelfand sequences, described by Hasse diagrams. In this paper, the authors present an alternative characterization of Hasse diagrams, which is quite efficient in the case of low gradings. Several examples are given.
This paper constitutes a summary of the author’s Ph.D. thesis [The cell complex construction and higher -torsion for bundles with framed Morse function (Brandeis Univ. 1989)]. Proofs of the results cited here will appear elsewhere.The first section is devoted to outlining a means of passing in a continuous way from the space of pairs , where is a compact smooth manifold and is a Morse function on , into a moduli space for finite cell complexes.In section two the results of section one are...
It is well-known that the question of existence of a star product on a Poisson manifold is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures of the following type with , for some .
Summary: All algebraic objects in this note will be considered over a fixed field of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95,...