TOWARDS A 2-DIMENSIONAL NOTION OF HOLONOMY

Küçük Resim Yok

Tarih

2022

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Amer Inst Mathematical Sciences-Aims

Erişim Hakkı

info:eu-repo/semantics/openAccess

Özet

Previous work (Pradines, C.R. Acad. Sci. Paris 263 (1966) 907, Aof and Brown, Topology Appl. 47 (1992) 97) has given a setting for a holonomy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for the crossed module case. The development also has to use corresponding notions for certain types of double groupoids. This leads to a holonomy Lie groupoid rather than double groupoid, but one which involves the 2-dimensional information.

Açıklama

Anahtar Kelimeler

Crossed module, homotopy, double groupoid, linear section, Lie groupoids, holonomy

Kaynak

Journal of Geometric Mechanics

WoS Q Değeri

Q4

Scopus Q Değeri

Q3

Cilt

14

Sayı

2

Künye