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- W2038898995 abstract "The gauge transformation group of a principal U(1)-bundle over a smooth manifold M is naturally isomorphic to the group C∞(M,U(1)) of U(1)-valued smooth functions on M , and is identified with the free loop group LU (1) in the case of M = S. The smooth Deligne cohomology groups ([2, 5, 7]) of M generalize C∞(M,U(1)), so that we can think of them as generalizations of LU (1). We notice that the idea of regarding smooth Deligne cohomology groups as generalizations of loop groups is natural from a viewpoint of “higher gerbes”. The notion of gerbes was introduced by Giraud [12]. One can think of gerbes as fiber bundles whose fibers are categories. Similarly, one can think of 2-gerbes, due to Breen [1], as fiber bundles whose fibers are so called 2-categories. At present, formulating general “higher gerbes” rigorously may remain as an issue to be studied. However, a cohomological argument allows us to grasp an outline of “higher abelian gerbes”. By the help of the argument, we can deduce that smooth Deligne cohomology groups realize “gauge transformation groups of higher abelian gerbes”, so that they provide generalizations of ordinary gauge transformation groups as well as loop groups. (A more detailed discussion of this deduction is given in [14].)" @default.
- W2038898995 created "2016-06-24" @default.
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- W2038898995 date "2007-08-01" @default.
- W2038898995 modified "2023-10-03" @default.
- W2038898995 title "Representations of gauge transformation groups of higher abelian gerbes" @default.
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- W2038898995 doi "https://doi.org/10.1142/9789812779649_0003" @default.
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