Yazar "Brown, R" seçeneğine göre listele

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    Homotopies and automorphisms of crossed modules of groupoids
    (Springer, 2003) Brown, R; Içen, I
    We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere.
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    Lie local subgroupoids and their holonomy and monodromy Lie groupoids
    (Elsevier Science Bv, 2001) Brown, R; Içen, I
    The notion of local equivalence relation on a topological space is generalized to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendability of local Lie morphisms. (C) 2001 Elsevier Science B.V. All rights reserved.
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    Local subgroupoids II
    (Elsevier, 2003) Brown, R; Içen, I; Mucuk, O
    The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal in the special case. These results are required for further applications to holonomy and monodromy. (C) 2002 Elsevier Science B.V. All rights reserved.
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    Towards a 2-dimensional notion of holonomy
    (Academic Press Inc Elsevier Science, 2003) Brown, R; Içen, I
    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.