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Let M be a real analytic manifold modeled on a locally convex space and K bea non-empty compact subset of M. We show that if an open neighborhood of K in Madmits a complexification which is a regular topological space, then the germof the latter (as a complex manifold) is uniquely determined. If M is regularand the complexified modeling space of M is normal, then a regularcomplexification exists for some neighborhood of K. For each (real or complex)analytic regular manifold M modeled on a metrizable locally convex space andBanach-Lie group H, this allows the group Germ(K,H) of germs of H-valuedanalytic maps around K in M to be turned into an analytic Lie group which isregular in Milnor's sense. A special case is a regular real analytic Lie groupstructure on the group of real analytic H-valued maps on a compact realanalytic manifold M (which, previously, had only been treated in the convenientsetting of analysis). Combining our results concerning groups of germs with anidea by Neeb and Wagemann, one can also obtain a regular Lie group structure onthe group of all real analytic H-valued mappings on the real line.

Complexifications of infinite-dimensional manifolds and new constructions of infinite-dimensional Lie groups