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Diez, T. (author), Rudolph, Gerd (author)
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proof is inspired by the Lyapunov–Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces. It uses a slice theorem for Fréchet manifolds...
journal article 2021
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Janssens, B. (author), Diez, T. (author), Neeb, Karl-Hermann (author), Vizman, Cornelia (author)
Let M be a manifold with a closed, integral (k+1)-form ω⁠, and let G be a Fréchet–Lie group acting on (M,ω)⁠. As a generalization of the Kostant–Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of g by R⁠, indexed by Hk−1(M,R)∗⁠. We show that the image of Hk−1(M,Z) in Hk−1(M,R)∗ corresponds to a...
journal article 2021