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Principal bundles on infinite dimensional manifolds with corners. (English) Zbl 0865.58004

The interesting paper under review proposes a “general theory of principal bundles over real Banach differentiable manifolds with corners”, by establishing a bijective correspondence between them and a special class of free Lie group actions over such manifolds. It includes some examples.
This is a continuation of the authors’ program to study transversality for maps of real Banach manifolds with corners, with which they proved a version of Thom’s transversality theorem. They have published their earlier results in Spanish and in English [the first two authors, ‘Differential topology’ (1988; Zbl 0633.57001) and (1992; Zbl 0760.57001)].

MSC:

58B25 Group structures and generalizations on infinite-dimensional manifolds
58A30 Vector distributions (subbundles of the tangent bundles)
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References:

[1] S. Armas-Gomez, J. Margalef-Roig, E. Outerelo-Dominguez and E. Padron-Fernandez, Embedding of an Urysohn differentiable manifold with corners in a real Banach space. Proceedings of the Winter School Geometry and Topology. SRNI (Czechoslovakia). Supplemento ai Rendiconti del Circolo Mat. di Palermo, Serie II, 30 (1993), 143-152. · Zbl 0871.57018
[2] D. Husemoller, Fibre Bundle (third edition), Springer-Verlag (1994).
[3] S. L. Lang, Differential Manifolds, Addison Wesley (1972).
[4] J. Margalef, E. Outerelo and E. Padron, On submersions preserving the boundary and quotient manifolds. Proc. of International Conference on Differential Geometry and its Applications (Brno, Czechoslovakia), World Scientific (1990), 119-128. · Zbl 0789.58007
[5] J. Margalef and E. Outerelo, Differential Topology, Math. Studies, 173, North Holand (1992). · Zbl 0760.57001
[6] J. Margalef and E. Outerelo, Lie group actions over manifolds with corners, Math. Japonica, 38 (1993), 577-582. · Zbl 0779.58009
[7] P. W. Michor, Manifolds of differential mappings, Shiva Math., 3 (1980). · Zbl 0433.58001
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