Towards a 2-dimensional notion of holonomy
Küçük Resim Yok
Tarih
2003
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Academic Press Inc Elsevier Science
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. (C) 2003 Elsevier Inc. All rights reserved.
Açıklama
Anahtar Kelimeler
crossed module, homotopy, double groupoid, linear section, Lie groupoids, holonomy
Kaynak
Advances in Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
N/A
Cilt
178
Sayı
1
