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We provide a model of the String group as a central extension of finite-dimensional
2–groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle
maps. This bicategory is a geometric incarnation of the bicategory of smooth
stacks and generalizes the more naive 2–category of Lie groupoids, smooth
functors, and smooth natural transformations. In particular this notion of
smooth 2–group subsumes the notion of Lie 2–group introduced by Baez and
Lauda [Theory Appl. Categ. 12 (2004) 423–491]. More precisely we classify a
large family of these central extensions in terms of the topological group
cohomology introduced by Segal [Symposia Mathematica, Vol. IV (INDAM,
Rome, 1968/69), Academic Press, London (1970) 377–387], and our String
2–group is a special case of such extensions. There is a nerve construction
which can be applied to these 2–groups to obtain a simplicial manifold,
allowing comparison with the model of Henriques [arXiv:math/0603563]. The
geometric realization is an A∞–space, and in the case of our model, has
the correct homotopy type of String(n). Unlike all previous models, our
construction takes place entirely within the framework of finite-dimensional
manifolds and Lie groupoids. Moreover within this context our model is
characterized by a strong uniqueness result. It is a canonical central extension of
Spin(n).
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