Smooth Extensions and Spaces of Smooth and Holomorphic Mappings

Details Smooth Extensions and Spaces of Smooth and Holomorphic Mappings Smooth Extensions and Spaces of Smooth and Holomorphic Mappings

2005-11-02

arxiv.org/abs/math/0511064v1

J. Geom. Symmetry Phys. 5 (2006) 118

Mathematics

Differential Geometry

10 pages

Scientific paper

In this paper we present another notion of a smooth manifold with corners and relate it to the commonly used concept in the literature. Afterwards we introduce complex manifolds with corners and show that if $M$ is a compact (respectively complex) manifold with corners and $K$ is a smooth (respectively complex) Lie group, then $C^{\infty}(M,K)$ (respectively $C^{\infty}_{\C}(M,K)$) is a smooth (respectively complex) Lie group.

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