2,002 reputation
817
bio website homepages.ulb.ac.be/~samulisi
location Nantes, France
age
visits member for 3 years, 6 months
seen Jun 13 at 12:28

Postdoc working in symplectic/contact topology. I'm currently at the Université de Nantes.


Feb
10
answered Why is the dividing set nonempty when a convex surface has Legendrian boundary?
Sep
24
comment Isotopy between two open disks on a surface
You're definitely on the right track. Not sure if this is the kind of hint you are looking for, but I would consider also a $U'$ that is a $2\epsilon$ neighbourhood of $P$. Then, you can find an isotopy that does nothing on $U$ and sends the annulus $A \setminus U$ to $U' \setminus U$.
Sep
24
revised What is nonhomogeneous linear mapping?
added more text from Milnor, making the quotation's context clearer.
Sep
24
suggested suggested edit on What is nonhomogeneous linear mapping?
Sep
24
comment What is nonhomogeneous linear mapping?
@studiosus: can you put that as an answer? The continuation of the text makes this clearer. I have taken the liberty of editing it in to the question, though it will wait for peer review.
Sep
18
comment Natural diffeomorphism between $T\mathbb{S}^n\times \mathbb{R}$ and $\mathbb{S}^n\times\mathbb{R}^{n+1}$
@OhMyGod: yes, that's the idea. The sphere sits inside of $\mathbb{R}^{n+1}$ (as the unit sphere, say). The tangent bundle of $\mathbb{R}^{n+1}$ (which is trivial), restricted to the sphere, can also be seen as the tangent bundle of the sphere summed with its normal bundle.
Sep
17
answered is any hamiltonian system with just one degree of freedom completely integrable?
Sep
16
comment a question about pre-symplectic manifold
Everywhere I have seen the term "presymplectic form" used, it means $\omega$ is closed and has constant rank.
Sep
16
answered Can the system $\partial_x f(x,y) = \dot{y}$, $\partial_y f(x,y) = \dot{x}$ be related to some Hamiltonian system?
Sep
16
answered Understanding the definition and meaning of cotangent space
Jul
25
answered symplectic strucutre
Jun
4
comment Prove that the circle $S^1$ is not the boundary of any compact manifold with boundary in $\mathbb R^2-{(0,0)}$
This point is clear from the question already, but I want to emphasize that when you say "the circle $S^1$", you mean the unit circle in $\mathbb R^2$. There are plenty of other embedded circles in $\mathbb R^2 \setminus \{ 0 \}$ that do bound disks (e.g. take the boundary of the disk of radius 2 centred at $(0, 500)$). In this problem, there is no ambiguity, but it is often useful to keep track of what you mean exactly. (In particular, after you have figured this out, a good exercise is to see the difference between my circle and your circle.)
May
31
comment Horn and spindle tori
This "slice" idea is not the right approach. You can easily construct a submanifold of $\mathbb{R}^3$ so that a coordinate slice (e.g. $z = const$) is not a submanifold for some suitable choice of constant. (Simple example: take a standard torus and choose a slice that gives you a figure 8). In your horn and spindle tori, you have points of self-intersection. Look at the neighbourhood of one of them. Does it look like a neighbourhood in a Euclidean space?
May
31
comment Horn and spindle tori
Can you define what the spindle torus and horn torus are?
May
29
comment Chern class of tautological line bundle
After you have done the computation this way, I think it would be instructive to see how Milnor-Stasheff do it. I learned a lot from working through that section of their book.
May
25
awarded  Enthusiast
May
24
revised Does this IVP have a unique solution for all $x \in \mathbb R$
added a sentence for clarity
May
24
comment Does this IVP have a unique solution for all $x \in \mathbb R$
@Tunococ: if you've cited a local uniqueness theorem, you've done all the necessary work to answer the question (see Artem's solution below). Ron, if you look at the example I give in my answer (with $y' = y^{2/3}$), you will see why I am somewhat concerned about how to provide a complete argument when you cross the singular points in your separation of variables. I'd think it was really cool if you could indeed provide the missing details in your argument to show global uniqueness -- if it worked, it would be a lower tech solution to the problem than any I know.
May
24
answered Does this IVP have a unique solution for all $x \in \mathbb R$
May
23
comment Does this IVP have a unique solution for all $x \in \mathbb R$
OK, perhaps this is a question of taste -- nothing you wrote is false. I do, however, feel this is misleading because the uniqueness of global solutions to this IVP has nothing to do with its separability. This is why I asked above what theorems the OP knew about existence/uniqueness.