Recent content by kakarotyjn

I think there is no need to read books of masters like Gauss or Newton, their masterpieces are too old to learn. You can learn Newton's work by taking the course Calculus, learn Gauss's work buy learning differential geometry or complex analysis or number theory. There is no need to read their...

Yes,it is good to watch the lecture.But it's pity that I can't watch some good videos in youtube in my place...

Since there no teacher doing geometry or topology in our school,I have to learn some course all by myself.But I often come upon problems when I'm reading the book or doing the exercises.In some exercises,I even don't know which part of book can be used to solve it. So I want to ask here hope...

Oh,I see.Every element is a finite linear combination of bases,so H^0(M)\otimes H^0(F) consist of finite sum of matrices.

Hi morphism! I'm still not clear why it is a finite linear combination \sum a_{ij} \, e_i \otimes f_j,since the bases \{ e_i \} and \{ f_i \} are infinite dimensional,so \{ e_i \otimes f_i \} should be infinite dimensional,isn't it? Thank you!

Let M and F each be the set Z^+ of all positive integers.So the de Rham Cohomolgoy H^0(M) and H^0(F) is infinite dimensional. But why does H^0(M)\otimes H^0(F) consist of finite sums of matrices (a_{ij}) of rank 1? Thank you!

I've take part in Math Olympiads in China when I'm a high school student.I learned by my self and got a book then read it.I found I fear every hard problem I met because I can't solve it,even don't know where to start to think.And I also feel it boring because Olympiads problems had less...

I want to save enough money to buy a Pelikan M400 to write math though I don't know how does it fells. It sells 1000 rmb in China.

Thank you lavinia! I can get a sketchy understand of the proof.There are some basic knowledge of transverse intersection I don't know.I will look at it.

Thank you lavinia and zhentil! To lavinia,I'm not very clear about some property of Euler class you listed,my foundation of topology is quite insufficient.The derivation of the global angular form for an oriented 2 plane bundle :by\frac{d\theta_\alpha}{2\pi}-\pi^* \ksi_\alpha=\frac{d...

I have read the section about sphere bundle in Differential Forms in Algebraic Topology,but I still don't understand the Euler class very clear.I don't know how to calculate it for a sphere bundle,for example the sphere bundle of S^2. And I can't work out the exercise at the end of the...

Hi lavinia! Why it winds twice around the circle then the local degree is 2?Thank you.

This is an example from Bott and Tu 's book DFAT(page 125).The example is in the image.I don't understand why can we get the local degree of the section s by constructing an vector field by parallel translation and calculate the rotating number of it.And why the local degree is 2? Could...

Maybe I ignore to explain that \pi:E\rightarrow M is a sphere bundle with structure group Diff (S^n)

Hi!The details is in the attached file. I don't understand the sentence which is bolded,why if we extend the D-cochain to a D-cocycle,then we can get a global form which restricts to the d-cohomology class? Any hints?Thank you!:smile: