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Zbl 1165.51005
Markl, Martin
Natural differential operators and graph complexes. (English)
[J] Differ. Geom. Appl. 27, No. 2, 257-278 (2009). ISSN 0926-2245

The aim of the paper is to present an original and non traditional approach to the study and classification of natural differential operators. In particular, the classification of natural operators corresponds to calculations of the cohomology of certain graph complexes. First, it is presented that the abstract tensor calculus is a useful language for the description of geometric objects. Then it is shown how results on graph complexes may give explicit classification of natural operators. As an example there are classified all natural operators on vector fields and also all natural operators on linear connections and vector fields, with values in vector fields.
[Miroslaw Doupovec (Brno)]

MSC 2000:: *51H25 Geometries with differentiable structure
18G35 Chain complexes (homological algebra)
58A32 Natural bundles

Keywords: natural differential operator; graph complex; cohomology; vector field; connection

Cited in: Zbl 1220.53019

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