Recent content by Calabi

OK I think it's OK:oldlaugh:. Thank you again both of you.

OK. I still reading my curse, maybe I'll saw this result. Because I don't see how to demonstrate it. Thank you for your precious help.

OK, not very clear with the link, but I get the main idea above. And the connected sum of projective plan miness point or not is it orientable or not?

Hello, thank you fresh_42 for uping the message and thank you Lavina. I find what you were talking about here : http://www.i2m.univ-amu.fr/perso/jean-baptiste.campesato/docs/memoireM2.pdf page 57 ans at the moment I wanted answer you already answer to me:oldlaugh:. Thanks. In my curse the...

I'm sorry if i did many mistakes, I'm french. I corrected the most I saw. If I didn't have answer could I post this on MathStack? I ask because ask a same question on several forum is a little bit rude.

I have Ideas with the thorus but I still got 2 unknown dimensions.

Hi, I'd like to compute the de Rham cohomology of the 3 following objects : -A connected sum of ##g \in \mathbb{N}## reals projectives plans ##P_{2}(\mathbb{R})##. -A connected sum of ##g \in \mathbb{N}## torus without ##n## points ##\mathbb{T}^{2} - \{x_{1}, x_{2}, ..., x_{n}\}##. - A...

What do you think please?

The derivate ##D## group of ##G' = G / Z(G)## is not always closed(so it's not necessarly a Lie Group for the induce topolgie.). So we must show that ##D## is closed. Then if we show that ##[T_{e}G', T_{e}G'] = T_{e}G'##(the equality is true because of semi simplicity.). is the tangent bundle of...

I saw in a book that if we add ##T_{e}G## semi simple it's work. It beginn the same ways as me by remarking ##Ad(G) \simeq G / Z(G)## is compact and is a Lie group because ##Z(G)## is discret. Then he claim that ##G / Z(G)## is equats to its derivate group and that it conclude. Do you see why?

Hello it's doesen't work. My goal is to show ##G## connected ##Ad(G)## compact and ##Z(G)## discret ##\Rightarrow ## ##G## compact and ##Z(G)## finite.

The things is that we use ##Ad(G)## compact only to show ##G / Z(G)## which is not enough. And the discret properties is not use too much.

OK. I understand a few things. But I'm not sure to be able to show what you said. Thanks a lot for your answer. If someone as idea I'll be pleased to listen it.

Then, the non existence on continuous homomorphism is not garanti.

Hello fresh_42, I consult the book in my University's library. I see the theorem but how to link to the first result I try to show? I remember I try to show ##Ad(G) \subset Gl(T_{e}G)## is compact and the center ## Z(G)## of ##G## is discret (just to remember, forall ##g \in G##, ##Ad(g) =...