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| bio | website | homepages.ulb.ac.be/~samulisi |
|---|---|---|
| location | Nantes, France | |
| age | ||
| visits | member for | 2 years, 2 months |
| seen | 2 hours ago | |
| stats | profile views | 283 |
Postdoc working in symplectic/contact topology. I'm currently at the Université de Nantes.
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Apr 8 |
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Vector fields as section of tangent bundle and what is $T_xM$ for you? I think this is what jerrysciencemath wanted to know. |
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Apr 8 |
answered | Structure on manifolds |
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Apr 8 |
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Structure on manifolds I don't understand what your second question means. Can you give some more details of what you are reading and/or looking to have clarified? |
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Apr 7 |
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Why is Cartan Formula just an avatar of Leibniz rule? @DamienL: I've written some details. I hope this helps explain that identity. |
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Apr 7 |
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Why is Cartan Formula just an avatar of Leibniz rule? added a proof of the key identity |
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Apr 4 |
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Floquet's Theory, Hills Equation Have you looked at the wikipedia page? en.wikipedia.org/wiki/Floquet_multiplier (Of course, to apply what they write, you will need to convert your second order equation to a first order system.) |
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Apr 4 |
answered | Why is Cartan Formula just an avatar of Leibniz rule? |
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Apr 1 |
answered | Algebraic interpretation of Lyapunov functions |
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Mar 29 |
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Why is Cartan Formula just an avatar of Leibniz rule? Thanks for the link to the video! Also, what Martin said is the answer. |
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Mar 29 |
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What is the sense of the equality sign =? Very nice explanation. I can go delete mine now. |
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Mar 27 |
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Winding number of vector field on surface It's not more general... what I described above really uses the fact that the structure group of the tangent bundle to an oriented surface can be reduced to U(1). This is not true for a general manifold. In some sense, what I describe can be generalized to a discussion of Maslov classes of Lagrangians in symplectic manifolds... but that's much fancier than what you are interested in. |
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Mar 26 |
answered | Winding number of vector field on surface |
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Mar 26 |
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Winding number of vector field on surface Do you know anything about the zeros of these vector fields? These can make the discussion a little tricky. |
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Mar 24 |
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How is the shape operator related to the second fundamental form? Can you say a bit more about what $L$, $M$ and $N$ are in your definition of the second fundamental form? In my mind, the second formulation you have is the definition, so I'd like a clearer idea of what your definition is. |
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Mar 22 |
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Show that $\Gamma(TM) \cong_{\mathbb{R}} \mathsf{Der}_{\mathbb{R}} C^{\infty}(M)$ My hint would be to think about what a derivation has to be, if you look at it in a coordinate chart. Another hint is to remember that you have cut-off functions and partitions of unity. |
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Mar 22 |
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Show that $\Gamma(TM) \cong_{\mathbb{R}} \mathsf{Der}_{\mathbb{R}} C^{\infty}(M)$ The existence of $\chi$ is key in differential geometry. See for instance en.wikipedia.org/wiki/Bump_function. |
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Mar 22 |
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Sections of the tensor product of two vector bundles I don't understand the question. Are you asking about how to understand the tensor product of two bundles as a vector bundle? |
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Mar 20 |
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How much of an $n$-dimensional manifold can we embed into $\mathbb{R}^n$? Another idea would be to take a Morse function with a unique minimum. Then, take the union of all the ascending manifolds from higher index critical points. This is of codimension 1 and thus of measure 0. I'm pretty sure the complement is the ascending manifold of the minimum and thus diffeomorphic to a ball. Oh, wait, that's the link that Jason gave. Sorry. |
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Mar 20 |
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Other definitions of orientation of a surface embedded in $\Bbb{R^3}$ What do you mean by the triangles of a surface? Are you given a triangulation of the surface to start with? or is this for any triangulation? |
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Mar 20 |
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what are the holomorphic curves in $T^{*}S^3$ with boundary on the zero section? added 1407 characters in body |
