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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

12 votes

Are submersions of differentiable manifolds flat morphisms?

I can show that this is true for your "simple" case. If g(x,y) ∈ C∞(ℝ2) vanishes on x ≤ 0 then it decomposes as g(x,y) = a(x)G(x,y) where a(x) ∈ C∞(ℝ) vanishes on x ≤ 0 and G(x,y) ∈ C∞(ℝ2). This …
George Lowther's user avatar
12 votes

Are submersions of differentiable manifolds flat morphisms?

I can get quite close to proving this. That doesn't mean that the result is true but it does at least seem to be very nearly true. We can also see what any counterexamples must look like if it does fa …
George Lowther's user avatar
15 votes

Big Picture: What is the connection of Malliavin calculus with differential geometry?

I can't speak for Paul Malliavin's influences, but I do know a bit about Hormander's theorem (by no means, an expert), and it is naturally suited to differentiable manifolds involving largely the idea …
George Lowther's user avatar