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dg.differential geometry – Example on pseudogroups
Definition:
A pseudo group is a collection $\mathcal{G}$ of (locally defined) invertible smooth diffeomorphisms of a manifold $M$. The simplest example of a pseudogroup is the collection of all local diffeomorphism of a manifold $M$.
Example:
Consider the infinitedimensional Lie pseudogroup
$$X=x,\qquad Y=y\,f(x)+\phi (x),\qquad Z=z(f(x))^x+\psi(x),$$
where $f,\phi,\psi\in C^\infty (\mathbb{R})$ other $f(x)>0$.
Obviously, $X,Y$ other $Z$ are the target coordinates. Indeed, the pseudogroup acts on the coordinate $(x,y,z)$ and transforms it to the target coordinates $(X,Y,Z)$.
My questions:

what are the group parameters??

If we split the cotangent bundle into horizontal and vertical forms, what are the vertical forms?
Reference
[1] Olver, Peter J.; Pohjanpelto, Juha; Valiquette, Francis, On the structure of Lie pseudogroups, SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 077, 14 p. (2009). ZBL1241.58008. [2] https://math.stackexchange.com/questions/4449167/exampleonpseudogroupswe will offer you the solution to dg.differential geometry – Example on pseudogroups question via our network which brings all the answers from multiple reliable sources.