Search Results

Yes, the Hodge decomposition is a topological decomposition with respect to the $C^\infty$-topology. One can argue, for example, that the Laplace-Beltrami $\Delta$ operator is elliptic and hence can b …

In finite dimensions, properness of the action is all you need for a slice theorem (and thus for the manifold structure of the quotient). However, in the Banach realm, properness is not enough. For ex …

The following textbooks contain a proof of the symplectic slice theorem: Juan-Pablo Ortega and Tudor S. Ratiu: Momentum Maps and Hamiltonian Reduction Gerd Rudolph and Matthias Schmidt: Differential …

The compressible case uses semidirect products of groups (group of diffeomorphisms times functions). To my knowledge, the first paper that discusses this in detail is Marsden, Ratiu, Weinstein: Semidi …

The most general definition I know is the following. Every fiberwise bilinear form $\eta: V_1 \times V_2 \to W$ of vector bundles $V_1, V_2, W$ over $M$ gives rise to the wedge product of vector-bundl …

Concerning your second point, it is no longer true that closed subgroups are Lie subgroups (even in the Hilbert setting). The corresponding result in infinite dimensions needs additional assumptions c …

Each of the different formalism of classical mechanics has its advantages and disadvantages. However, in the end all three frameworks tend to be equivalent, and thus the following list is very subject …

Let $E \to M$ be a smooth fiber bundle. Instead of differential forms defined on the whole tangent bundle $TE$ one could also consider forms on the vertical tangent bundle $VE$, i.e. forms defined on …

If you know German, then I strongly recommend you the Habilitation thesis of Markus Pflaum: "Ein Beitrag zur Geometrie und Analysis auf stratifizierten Räumen" for the stratification of the orbit spa …

It is well-known that a linear differential equation in a finite-dimensional vector space depends continuously on some external parameters (for details see below). I search for an explicit reference w …

As the non-uniques of a quantization scheme was already brought up, I will add a nice resource which gives a broad overview of different techniques: Quantization Methods: A Guide for Physicists and A …