Orbit projections of proper Lie groupoids as fibrations
Let be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection is a fibration if and only if is regular.
Orbit projections as fibrations
The orbit projection of a proper -manifold is a fibration if and only if all points in are regular. Under additional assumptions we show that is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: is a -quasifibration if and only if all points are regular.
Composition in ultradifferentiable classes
We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space and the Roumieu space as intersection and union of spaces and for associated weight sequences, respectively.
Singular Poisson reduction of cotangent bundles.
We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.
Choosing roots of polynomials with symmetries smoothly.
Lifting smooth curves over invariants for representations of compact Lie groups. II.
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