Covariant Approach to Weil Bundles

KOLÁŘ, Ivan. Covariant Approach to Weil Bundles. 1st ed. Brno: Masarykova univerzita, 2016, 106 pp. ISBN 978-80-210-8385-1.

Basic information

Original name

Covariant Approach to Weil Bundles

Name in Czech

Kovariantní přístup k Weilovým bandlům

Authors

KOLÁŘ, Ivan

Edition

1. vyd. Brno, 106 pp. 2016

Publisher

Masarykova univerzita

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Other information

Language

English

Type of outcome

Book on a specialized topic

Field of Study

10101 Pure mathematics

Country of publisher

Czech Republic

Confidentiality degree

is not subject to a state or trade secret

Publication form

printed version "print"

ISBN

978-80-210-8385-1

Tags

Munipress

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Abstract

In the original language

In the original definition by A. Weil, an infinitely near point on a smooth manifold M is introduced as a homomorphisms of the algebra of smooth functions C^\infty on M into a local (=Weil) algebra A. This point of view is close to algebraic geometry. On the other hand, there is the idea of (k; r)-velocity based on the concept of jet by C. Ehresmann, that seems to be more appropriate for differential geometry. The author introduces an original concept of A-velocity, that unifies both points of view. Beside the geometry of Weil bundles, some further jet-like functors are studied. The last Chapter 8 is devoted to nonholonomic jets, non-holonomic contact elemets and their applications to the submanifolds of Cartan spaces.

In Czech

Kniha se zabývá původním konceptem A. Weila, který odpovídá algebraické geometrii, a alternativnim konceptem C. Ehresmanna, který má blíže k diferenciální geometrii. Následně představuje svůj vlastní koncept A-rychlosti, který oba náhledy sjednocuje.