Graded jet geometry
type: Item
instance of: scholarly article
title: Graded jet geometry
author: Jan Vysoký
published in: Journal of Geometry and Physics
publication date: 2024-09-02T00:00:00Z
review text: The aim of the paper is to generalize jet geometry to \(\mathbb Z\)-graded bundles. In particular, the author constructs the \(k\)-th order jet bundle of an arbitrary \(\mathbb Z\)-graded vector bundle \(\mathcal E\) over an arbitrary \(\mathbb Z\)-graded manifold \(\mathcal M\). The construction is based on the description of graded bundles in terms of sheaves of sections.
reviewed by: Miroslav Doupovec
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 7904721
zbMATH Keywords: jet manifolds
zbMATH Keywords: graded manifolds
zbMATH Keywords: graded vector bundles
zbMATH Keywords: jet vector bundles
MaRDI profile type: Publication
cites work: Q4238949
cites work: INTRODUCTION TO SUPERGEOMETRY
cites work: Q5821617
cites work: Introduction to graded geometry
cites work: Q4864707
cites work: Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology
cites work: Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
cites work: Global variational calculus on graded manifolds. I: Graded jet bundles, structure 1-form and graded infinitesimal contact transformations
cites work: Deformation quantization of Poisson manifolds
cites work: The category of \(\mathbb{Z}\)-graded manifolds: what happens if you do not stay positive
cites work: Q3998623
cites work: Q4015797
cites work: Q4036986
cites work: THE POINCARÉ–CARTAN FORM IN SUPERFIELD THEORY
cites work: Smooth Manifolds and Observables
cites work: Seminar on Atiyah-Singer Index Theorem. (AM-57)
cites work: GRADED INFINITE ORDER JET MANIFOLDS
cites work: Graded Lagrangian formalism
cites work: Differential calculus on \(\mathbb{N}\)-graded manifolds
cites work: Q3994886
cites work: Graded Geometry, Q‐Manifolds, and Microformal Geometry
cites work: Graded generalized geometry
cites work: Global theory of graded manifolds
DOI: 10.1016/J.GEOMPHYS.2024.105250
description: scientific article; zbMATH DE number 7904721