منابع مشابه
1 Towards a 2 - dimensional notion of holonomy ∗
Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holon-omy 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 t...
متن کاملOn 2-Dimensional Holonomy
We define the fundamental strict categorical group P2(M, ∗) of a based smooth manifold (M, ∗) and construct categorical holonomies, being smooth morphisms P2(M, ∗) → C(G), where C(G) is a Lie categorical group, by using a notion of categorical connections, which we define. As a result, we are able to define Wilson spheres in this context.
متن کاملTowards a classification of Lorentzian holonomy groups
If the holonomy representation of an (n + 2)–dimensional simply-connected Lorentzian manifold (M,h) admits a degenerate invariant subspace its holonomy group is contained in the parabolic group (R×SO(n))⋉R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(M,h)) and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this...
متن کاملOn Two-Dimensional Holonomy
We define the thin fundamental categorical group P2(M, ∗) of a based smooth manifold (M, ∗) as the categorical group whose objects are rank-1 homotopy classes of based loops on M , and whose morphisms are rank2 homotopy classes of homotopies between based loops on M . Here two maps are rank-n homotopic, when the rank of the differential of the homotopy between them equals n. Let C(G) be a Lie c...
متن کاملTwo-dimensional Markovian Holonomy Fields
— We define a notion of Markov process indexed by curves drawn on a compact surface and taking its values in a compact Lie group. We call such a process a two-dimensional Markovian holonomy field. The prototype of this class of processes, and the only one to have been constructed before the present work, is the canonical process under the Yang-Mills measure, first defined by Ambar Sengupta [32]...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2003
ISSN: 0001-8708
DOI: 10.1016/s0001-8708(02)00074-9