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olivier dot begassat dot cours at gmail dot com


1d
comment Prove the automorphism given by $\phi \left(g\right)=\left(g^{-1}\right)^t$ is not an inner automorphism of $SL_n\left(R\right)$
@JyrkiLahtonen I included your comment in my answer.
1d
comment How to understand $d^2=0$ in differential form?
@Surb I think you can get away with twice differentiable at a point. That is, $f$ differentiable on some neighborhood of $p$, and its differential $Tf$ differentiable at $p$.
1d
comment How to understand $d^2=0$ in differential form?
For functions, it expresses the fact that the second derivative is symmetric, i.e., in local coordinates, $$\frac{\partial^2f}{\partial x^i\partial x^j}=\frac{\partial^2f}{\partial x^j\partial x^i}$$ I would also like an interpretation for higher forms.
2d
comment When is a vector field on a manifold restricted to a submanifold $X$ a vector field on $X$?
Your claim that the projection is independent of the Riemannian metric is false! Projection means projecting parallel to the orthogonal complement of $T_xX$ inside the euclidean space $(T_xM,g_x)$: this orthogonal complement may be different for different inner products.
2d
comment Automorphisms of the field of real numbers
@Crostul What do you mean when you write "you cannot define the field of real numbers in a purely algebraic way"?
2d
comment Automorphisms of the field of real numbers
There is only one (the identity). Here are hints on how to prove this: first show that any such automorphism fixes all rational numbers, and then prove that it respects the order on the real numbers. To do so, remember that a number is positive iff it is a square.
2d
comment Is $\mathbb{C}\bigotimes_\mathbb{R}\mathbb{C}\simeq \mathbb{C}\bigotimes_{\mathbb{C}}\mathbb{C}$?
This same question was asked less than a month ago, it's most definitely a duplicate.
2d
comment Group with topology which is not topological group
Consider $\Bbb Z/3\Bbb Z$ with the topology whose only non-trivial open set is $\lbrace 1\rbrace$.
Nov
24
comment Are compact complete geodesics closed?
There is a mistake elsewhere I don't know if it can be fixed.
Nov
24
comment Are compact complete geodesics closed?
@tedshifrin I don't need transversality per se, I only want $T_{(t,t')}c\times c(T_{(t,t')}\Bbb R\times\Bbb R)\oplus T\Delta_M$.
Nov
24
comment Irrational number inequality : $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}>\sqrt{3}$
Since both sides are positive, you can square everything...
Nov
24
comment Topological structure of the Manifold valued functions
Does any part need explaining? I don't suspect there'd be any difficulty in making this sketch formal. You'll need to invoke the Lebesgue covering lemma for $I$ at some point, but otherwise, this is it. The only point I'm not quite clear about is how to prove that any manifold admits a complete riemannian metric. But this is classical, and can be looked up.
Nov
24
comment is configuration space an H-space?
Doesn't look like it, because of the fundamental group being non-commutative (for $n\geq 3$).
Nov
23
comment $\lim p(n) = $? where p is a permutations on natural numbers
Prove directly that for any integer $N$, there is an integer $n_0$ such that for all $n\geq n_0$, $p_n\geq N$. This shows that $p$ has a limit at infinity, and $$\lim_{n\to\infty} p(n)=+\infty$$
Nov
23
comment $\lim p(n) = $? where p is a permutations on natural numbers
That assumes the existence of the limit (not that it's hard to prove).
Nov
21
comment Removing a open set from a finite open covering of a Normal space.
I don't know whether the statement is true or not.
Nov
21
comment Removing a open set from a finite open covering of a Normal space.
You will have to look for non-metrizable counter examples.
Nov
21
comment Removing a open set from a finite open covering of a Normal space.
You are asking whether an open subset of a normal space is still normal...
Nov
18
comment Another question in Bott-Tu.
Could you add the relevant details for those of us who don't have the reference handy? What is $\pi$?
Nov
17
comment Adjoint Operator of a Compact Operator
Take the time to write down an answer!