An implicit function theorem for Banach spaces and some applications

Details An implicit function theorem for Banach spaces and some applications An implicit function theorem for Banach spaces and some applications

2007-03-23

arxiv.org/abs/math/0703710v1

Mathematics

Group Theory

24 pages

Scientific paper

We prove a generalized implicit function theorem for Banach spaces, without
the usual assumption that the subspaces involved being complemented. Then we
apply it to the problem of parametrization of fibers of differentiable maps,
the Lie subgroup problem for Banach-Lie groups, as well as Weil's local
rigidity for homomorphisms from finitely generated groups to Banach-Lie groups.

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