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| bio | website | |
|---|---|---|
| location | Moscow, Russia | |
| age | ||
| visits | member for | 2 years, 10 months |
| seen | 14 mins ago | |
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umagon at google mail
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Nov 26 |
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Vanishing of the second Stiefel–Whitney classes of orientable surfaces @Anirbit Are you sure, you need this? Spin structures on a Riemann surface are in bijection with "halves" of the canonical class. So there are always exactly $2^{2g}$ (think of 2-torsion in the Jacobian) spin structures on a Riemann surface of genus $g$. |
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Nov 26 |
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Euler characteristic of sphere with a hole Unlike the analytic formula, formula $2-2g-b$ for Euler char works for surfaces without boundary nicely, missing condition here is compactness. |
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Nov 25 |
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Are finite indecomposable groups necessarily simple? @Jawad AFAICS, if G is indecomposable the decomposition from the theorem consists of one indecomposable subgroup, namely G itself |
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Nov 25 |
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String and BString Why, there is an infinite Postnikov tower (FiveBrane is a 7-connected cover but there is a 8-connected cover and so on). |
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Nov 23 |
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String and BString Some explanations: golem.ph.utexas.edu/category/2008/10/… (and links there) |
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Nov 23 |
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String and BString Related: math.stackexchange.com/q/46306/152. But there is a problem here: String is not a Lie group. |
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Nov 20 |
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Topological group: Multiplying two loops is homotopic to linking these paths? I agree. (But something like more explicitly would seem more... precise, indeed.) |
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Nov 20 |
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Topological group: Multiplying two loops is homotopic to linking these paths? Well, that's just E-H argument for this situation written down explicitly, isn't it?.. |
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Nov 19 |
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The long exact sequence of compact manifold @SteveD $M$ should be orientable and $1$ means fundamental class, I guess (the answer is "yes" than). |
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Nov 19 |
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Conjugation in fundamental group Hint: $\pi_1$ is also defined in terms of loops in $X$ — so what's the difference b/w $\pi_1(X)$ and $[S^1,X]$?.. |
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Nov 15 |
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Solving the recurrence relation $A_n=n!+\sum_{i=1}^n{n\choose i}A_{n-i}$ Have you tried entering first few terms in OEIS?.. |
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Nov 15 |
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Is there a way to establish a correspondence between the vector bundles over a torus and some kind of homotopy groups, just as we do to spheres @JasonDeVito Oh, you're right! It's, actually, not hard to show now that (for any surface $S$) $Vect_n(S)=H^1(S;\pi_0 GL_n)\oplus H^2(S;\pi_1 GL_n)$ (cf. AHSS). |
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Nov 15 |
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How to compute homotopy classes of maps on the 2-torus? @lethe Hope, the update explains something. |
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Nov 14 |
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Is there a way to establish a correspondence between the vector bundles over a torus and some kind of homotopy groups, just as we do to spheres BTW, can someone prove that the answer is the same as for $S^1\vee S^1\vee S^2$? (The latter space is stably homotopy equivalent to the torus, so at least in the stable range everything follows from Bott periodicity etc. But surely there should be more elementary proof?) |
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Nov 14 |
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Is there a way to establish a correspondence between the vector bundles over a torus and some kind of homotopy groups, just as we do to spheres (An idea I failed to implement correctly: use Künneth theorem for K-theory.) |
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Nov 9 |
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How do you format a logarithm's base in Stack Exchange? See meta.math.stackexchange.com/questions/107/… |
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Nov 4 |
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What is importance of the Bunyakovsky conjecture? @GerryMyerson Yes, I consider "how important do you consider the answer to this problem" to be too soft (as in "not a good fit to our Q&A format: <...> will likely solicit opinion <...>'"). |
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Nov 4 |
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Probability that a stick randomly broken in two places can form a triangle related: math.stackexchange.com/questions/1400/… |
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Oct 23 |
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the number of loops on lattice? @quantumelixir See updated version. |
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Oct 22 |
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What are these theta functions appearing in Sloane's database mathworld.wolfram.com/JacobiThetaFunctions.html, I guess |
