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| bio | website | |
|---|---|---|
| location | Moscow, Russia | |
| age | ||
| visits | member for | 2 years, 10 months |
| seen | 3 hours ago | |
| stats | profile views | 1,172 |
umagon at google mail
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Dec 1 |
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Higher Dimensional equivalent of genus Betti numbers (aka ranks of homology groups) is, perhaps, closest thing to what you're looking for. |
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Dec 1 |
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Higher Dimensional equivalent of genus There are, actually, many ways to generalize the notion of genus to higher dimensions: Betti numbers and Heegaard genus in algebraic topology, arithmetic and geometric genus in algebraic geometry... |
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Dec 1 |
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How to Make This Functor $H_n(X;\mathbb{Z}/2)$? Despite looking almost identical, the diagram for the torus has only 1 vertex and the diagram for $\mathbb RP^2$ has 2 vertices. Hence different homology. |
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Dec 1 |
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The derivative is a real limit? @Micro Oh... what would be really useful is some reference. Unfortunately I know nothing about English-language calculus text(book)s (and Knuth's comment suggests that maybe there is some problem here), but maybe someone else could help. |
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Nov 29 |
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Quiver describing perverse sheaves on $\mathbb C$ I don't know the name, but it's discussed @ mathoverflow.net/questions/31595/… |
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Nov 29 |
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What lies beyond the Sedenions AFAICS, arxiv.org/abs/1010.2156 claims to answer OPs last question |
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Nov 29 |
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The derivative is a real limit? @Micro Let me stress, that this "little-o-style definition" is precisely equivalent to the "limit-style definition" -- so if a function has derivative it can be approximated by a linear function. But, of course, finding such an approximation is not always that easy (compared to what you describe in your post). For example $e^h$ is $1+h+o(h)$ but it's quite non-trivial theorem (which one can't prove just by writing down all terms and throwing away higher-order ones). |
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Nov 29 |
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The derivative is a real limit? An example, where thinking in terms of linear approximation is especially convenient: math.stackexchange.com/a/3105 |
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Nov 28 |
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Octonionic Hopf fibration and $\mathbb HP^3$ (related: mathoverflow.net/questions/14698) |
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Nov 28 |
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What lies beyond the Sedenions (somewhat) related: mathoverflow.net/questions/19929/19975#19975 |
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Nov 28 |
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How do you integrate imaginary numbers? @ZevChonoles Huh? Notation like $\mathbb Z[\sqrt{-5}]$ for rings and (say) $1+\sqrt{-5}$ for elements of such rings is absolutely standard. |
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Nov 28 |
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How do you integrate imaginary numbers? @ZevChonoles I don't see the problem (there is completely general definition $R(\sqrt d):=R[x]/(x^2-d)$, if you wish) |
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Nov 28 |
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The Barber Paradox — A proposed set-theoretic approach Doesn't look like a question to me. |
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Nov 27 |
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Cohomology of $\mathbb RP^{n}$ with $\mathbb Z_2$ coefficients @palio That's incorrect. (Have you read the Wikipedia page you're linking to?..) |
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Nov 27 |
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Cohomology of $\mathbb RP^{n}$ with $\mathbb Z_2$ coefficients (Re: second part) how do you compute $H_i(RP^n;\mathbb Z/2)$? |
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Nov 26 |
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Properties preserved by diffeomorphisms but not by homeomorphisms @lurscher Exactly: every diffeomorphism is a homeomorphism, but not every homeomorphism is a diffeomorphism. So there can be some properties preserved by diffeomorphisms but not by (some non-smooth) homeomorphisms. |
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Nov 26 |
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Properties preserved by diffeomorphisms but not by homeomorphisms Julia sets are not manifolds (but nice example anyway) |
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Nov 26 |
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Vanishing of the second Stiefel–Whitney classes of orientable surfaces (Anyway, $\chi=w_n\mod 2$ is the Property 9.5 in Milnor-Stasheff's «Characteristic classes».) |
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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. |
