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I messed up slightly: i had forgotten that there was already a stub titled contact geometry. Now I have created contact manifold with some content that might better be at contact geometry. I should fix this. But not right now.
Why ? Contact manifold is not the only setup for contact geometry. There are e.g. contact orbifolds etc. IMHO the definitions about contact manifolds should be there. Like we do not have smooth manifold under differential geometry, but separately, though at present differential geometry entry dwells too much about formalisms for the space in which to do differential geometry than about basic ideas, problems and results of differential geometry per se.
Thus I think having two separate entries as it is now is long term beneficial, and no need to apologize.
Yes, but some of the general stuff, for instance the references, that is currently only at contact manifold should be (also) at contact geometry.
Good, I misundersttood that you wanted to merge the entries.
Is this of interest?
Looks interesting, would have to explore the possible applications of this multi-contact geometry a bit further. Personally I am fond of the fact that regular contact manifolds are “just” the total spaces of pre-quantizations of symplectic manifolds. But i have to admit that I don’t have a very detailed feeling for how restrictive regularity is for people working in contact geometry.
Otherwise, this is maybe a good opportunity to highlight again the fun fact that indeed to every closed $n+1$-form on any manifold, there is associated a Poisson bracket Lie n-algebra. For each and every. In particular if one can complete a multi-contact structure to a multisymplectic structure, then this applies and there we go.
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