Recent content by simeonsen_bg

There is a famous lecture by V.I.Arnold concerning the subject. http://neon7.110mb.com/On%20teaching%20mathematics.pdf

You may be right. Let me notice that by the Whitney embedding theorem every smooth n-manifold embeds smoothly in 2n-Euclidean space. So your second condition is superfluous. Now, as your manifold is orientable with w2=0, it is a spin manifold. And that’s what i found in a book by Stephen...

[Sorry, I confused in fact 'spin' with 'symplectic'.] from MathWorld: 'A spin structure exists if and only if the second Stiefel-Whitney class w2 of the tangent bundle of the manifold vanishes.' So, it is enough to find a spin 4-manifold with b_2 odd to complete the example. I am...

Cp^2

I suppose, you have to consider functions uniformely bounded by some constant M (or even vith uniformely bounded variation?), otherwise the whole set gets infinite measure, not 1, the way you described the measure.

So, we have a degree 1 map h from RP(3) to RP(3) that annihilates the generator of H_1(RP(3)) = Z_2 and are looking for a contradiction? I suppose it possible to get by considering the cohomology algebra of RP(3) with coefficients in Z_2 and the induced homomorphism h^*. As Z_2 is a...

f_k are arbitrary functions from the naturals into itself.

Hi, I have a sequence f_k(n) of functions N-->N, k=1,2... and I need to find a function f(n) growing faster than any f_k, i.e. f_k(n)/f(n) --> 0 as n-->infinity for any k. Is it possible and how can it be done?

Wouldn’t it be easier to take a flow on S^2 that is not area-preserving? So is for example a gradient flow with 2 fixed points - source and sink. Then it cannot be a symplectic one, as any symplectic flow is volume-preserving. (http://homepages.cwi.nl/~jason/Classes/numwisk/ch16.pdf)