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Remarks on infinite-dimensional Lie groups. (English) Zbl 0594.22009
Relativité, groupes et topologie II, Les Houches Éc. d’Eté Phys. Théor., Sess. 40, 1983, 1007-1057 (1984).
[For the entire collection see Zbl 0583.00023.]
This is a splendid and lucid account of infinite-dimensional Lie groups. I strongly recommend it to anyone with an interest in Lie groups, finite- dimensional or infinite-dimensional. The author discusses locally convex vector spaces, differential calculus, smooth manifolds and vector fields, Lie groups, diffeomorphism groups, the exponential map and product integrals, from Lie algebra to Lie group, non-analyticity of Diff(M), some homotopy groups of Lie groups.
Reviewer: R.J.Plymen

MSC:
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
57T20 Homotopy groups of topological groups and homogeneous spaces