Publication result detail

Description of jet like functors on vector bundles by means of module bundle functors on the bases

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

Original Title

Description of jet like functors on vector bundles by means of module bundle functors on the bases

English Title

Description of jet like functors on vector bundles by means of module bundle functors on the bases

Type

WoS Article

Original Abstract

Let C be an admissible category over manifolds and VBC be the category of vector bundles with bases being C-objects and vector bundle maps with base maps being C-maps. Assume that any C-morphism is a local isomorphism. We describe all jet like functors (i.e. fiber product preserving gauge bundle functors) of order r on VBC by means of Jr(-, R)-module bundle functors on C. Then we describe all jet like functors of vertical type of order r on VBC by means of vector bundle functors on C of order r. As an application we classify jet like functors of some type on VBm. Finally, we determine all natural Jr(M, R)-module bundle structures on the vector bundles JrE -* M and JrvE -* M, where E -* M is a vector bundle with m-dimensional basis and m >= 2.

English abstract

Let C be an admissible category over manifolds and VBC be the category of vector bundles with bases being C-objects and vector bundle maps with base maps being C-maps. Assume that any C-morphism is a local isomorphism. We describe all jet like functors (i.e. fiber product preserving gauge bundle functors) of order r on VBC by means of Jr(-, R)-module bundle functors on C. Then we describe all jet like functors of vertical type of order r on VBC by means of vector bundle functors on C of order r. As an application we classify jet like functors of some type on VBm. Finally, we determine all natural Jr(M, R)-module bundle structures on the vector bundles JrE -* M and JrvE -* M, where E -* M is a vector bundle with m-dimensional basis and m >= 2.

Keywords

(gauge) bundle functor; vector bundle; module bundle; jet

Key words in English

(gauge) bundle functor; vector bundle; module bundle; jet

Authors

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

RIV year

2025

Released

01.01.2024

Publisher

UNIV NIS, FAC SCI MATH

Location

NIS

ISBN

0354-5180

Periodical

Filomat

Volume

38

Number

1

State

Republic of Serbia

Pages from

241

Pages to

260

Pages count

20

URL

https://www.pmf.ni.ac.rs/filomat-content/2024/38-1/38-1-18-20303.pdf

BibTex

@article{BUT187399,
  author="Miroslav {Doupovec} and Jan {Kurek} and Wlodzimierz {Mikulski}",
  title="Description of jet like functors on vector bundles by means of module bundle functors on the bases",
  journal="Filomat",
  year="2024",
  volume="38",
  number="1",
  pages="241--260",
  doi="10.2298/FIL2401241D",
  issn="0354-5180",
  url="https://www.pmf.ni.ac.rs/filomat-content/2024/38-1/38-1-18-20303.pdf"
}