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A note on the holonomy of connections in twisted bundles. (English) Zbl 1067.58003

Summary: Twisted vector bundles with connections have appeared in several places. In this note the author considers twisted principal bundles with connections and studies their holonomy, which turns out to be most naturally formulated in terms of functors between categorical groups.

MSC:

58A99 General theory of differentiable manifolds
58A32 Natural bundles
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References:

[1] J.W. Barrett . Holonomy and path structures in general relativity and Yang-Mills theory . Int. J. Theor. Phys. , 30 ( 9 ): 1171 - 1215 , 1991 . MR 1122025 | Zbl 0728.53055 · Zbl 0728.53055 · doi:10.1007/BF00671007
[2] P. Bouwknegt and V. Mathai . D-branes, B-fields and twisted K-theory . J. High Energy Phys. , 3 , Paper 7, 2000 . MR 1756434 | Zbl 0959.81037 · Zbl 0959.81037 · doi:10.1088/1126-6708/2000/03/007
[3] R. Brown and C.B. Spencer G-groupoids, crossed modules and the fundamental groupoid of a topological group . Nederl. Akad. Wetensch. Proc. Ser. A79 , 38 ( 4 ): 296 - 302 , 1976 . MR 419643 | Zbl 0333.55011 · Zbl 0333.55011
[4] J-W. Brylinski . Loop spaces, characteristic classes and geometric quantization, volume 107 of Progress in Mathematics . Birkhauser , 1993 . MR 1197353 | Zbl 0823.55002 · Zbl 0823.55002
[5] A. Caetano and R.F. Picken . An axiomatic definition of holonomy . Int. J. Math. , 5 ( 6 ): 835 - 848 , 1994 . MR 1298997 | Zbl 0816.53016 · Zbl 0816.53016 · doi:10.1142/S0129167X94000425
[6] A. Caetano and R.F. Picken . On a family of topological invariants similar to homotopy groups . Rend. Ist. Mat. Univ. Trieste , 30 ( 1 - 2 ): 81 - 90 , 1998 . MR 1704827 | Zbl 0935.55006 · Zbl 0935.55006
[7] D.S. Chatterjee . On gerbs. PhD thesis , University of Cambridge , 1998 .
[8] A. Kapustin . D-branes in a topologically nontrivial B-field . Adv. Theor. Math. Phys. , 4 ( 1 ): 127 - 154 , 2000 . MR 1807598 | Zbl 0992.81059 · Zbl 0992.81059
[9] M.A. Mackaay and R.F. Picken . Holonomy and parallel transport for Abelian gerbes . To appear in Adv. Math. Preprint available as math.DG/0007053. arXiv | MR 1932333 | Zbl 1034.53051 · Zbl 1034.53051 · doi:10.1006/aima.2002.2085
[10] K. Mackenzie . Lie groupoids and Lie algebroids in differential geometry . London Mathematical Society Lecture Note Series, 124 . Cambridge University Press , Cambridge , 1987 . MR 896907 | Zbl 0683.53029 · Zbl 0683.53029
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