Mariano Suárez-Alvarez
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Registered User
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57m |
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What is an interpretation of the relation in the cohomology of the pure braid groups? One you notice that those forms are closed (and considering those forms is very natural once you see that you are working with an arrangement of hyperplanes), the relations of Arnold are the very first that come to mind. Why would one conjecture that these are all relations, I don't know, but that these forms generate the whole thing is a sensible optimistic guess —although Arnold surely had reasons too. |
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1d |
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What is the 31th homotopy group of the 2 - sphere ? «For separable states, the original Hilbert space $S^7$ simplifies to $S^2\times S^2$» Reading physics papers requires a lot of restraint :-) |
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1d |
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Reference request: Riemannian manifold of linear isometries from $\mathbb{C}^n$ into $\mathbb{C}^m$ @Tysin, it is clear that your question is not sufficiently transparent as to what exactly it is asking for —maybe elaborating more on what you are looking for will make it easier for you to find it. Your comment here is also rather opaque :-) |
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1d |
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What is the 31th homotopy group of the 2 - sphere ? But there is no fourth Hopf fibration! |
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1d |
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What is the 31th homotopy group of the 2 - sphere ? In what way the two things you list as motivation are motivation for asking what the 31st homotopy group is? |
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2d |
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A catalog of faithful representations of finite groups? There is no need of the «with repetitions» part: the smallest faithful reps are always multiplicity free. |
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May 15 |
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A catalog of faithful representations of finite groups? At the very least, explain what you mean by noteworthy... |
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May 15 |
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Special automorphisms of extraspecial groups @John, as soon as you get 50 points of reputation you will be able to add comments. Using the answer box to respond to someone's answer does not work at all. |
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May 14 |
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Awfully sophisticated proof for simple facts (You can avoid the strange substraction of two equal numbers in the end by using the reduced Euler characteristic; this is a standard trick) This of course subjective, as it depends on one's background, but this does not seem awfully sophisticated at all to me and, instead, appears quite natural! :-) |
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May 13 |
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What is the “fundamental theorem of invariant theory” ? This question reminds me of the Jabberwocky poem :-) |
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May 13 |
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Proper actions on unitary spheres of a Hilbert space Every torsion free discrete group $G$ acts properly and discontinuousy on the unit sphere of $L^2(G)$, no? |
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May 13 |
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Isomorphic maximal commutative semi-simple sub algebras of M_n(C). Don't ask questions in answer boxes (!) If you want another question, ask a new question. |
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May 13 |
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If $M_n(R)$ and $M_m(R)$ satisfy the same polynomial identities is it true that $m=n$? @Thiago, I was just providing an example to Pasha's second paragraph, quite independently of what the question asked for. |
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May 12 |
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Is there an analogue of curvature in algebraic geometry? Well, in order to get an isomorphism, you changed both the domain and the codomain of the map. The original domain and codomains had certain interest of their own, so the fact that after redefining things you do get an isomorphism may be not as useful as it may appear initially when seem from the point of view of the contexts where the question originally arose :-) |
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May 12 |
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Normal regular sequence in noncommutative algebras If you explained what is that «some result» in the homogeneous case, it might be easier to see what you are after in the general case. |
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May 12 |
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Is there an easy way to write down the singular cohomology of a hypersurface in a toric variety? Your question specializes to «is there a simple way of writing down the singular cohomology of a hypersurface in $P^n$?» One can compute the dimensions of the rational cohomology groups if the surface is smooth, I think, but I don't know if the ring structure comes out as easily. |
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May 12 |
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H^d[U(1)^n,U(1)] of the Borel cohomology and Chern-Simons theory I for one still don't know what cohomology you are talking aboout —Konrad asked you to be specific about this a few weeks ago but you haven't answered that afaict. Without knowing that, it is simply impossible to even make sense of what you are asking! For example, the answer by Henr.L below seems to have decided that you are taking about singular cohomology of the space $U(1)^n$, which I think is quite surely no the case... |
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May 11 |
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A characterization of Hilbert spaces? Dear Wlodzimierz, you can find formatting tips on this page htpp://mathoverflow.net/editing-help; in particular, a common way to get a link you have to use the syntax [some text](the actual URL). I hope your time on MO is not that bad, because I for one enjoy very much reading your contributions! |
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May 11 |
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Resolutions of Lie algebras Can't you just copy what Tate did? Pick a presentation; start with the free Lie algebra on the generators, add a generators $y$ of degree $1$ per relation $r$, and define $d(y)=r$. Find generators for the homology of this dg, lift them to cycles, add generators to kill them and so on. |
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May 11 |
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non-convex Polytope definition. There are various definitions of what regularity should mean in Coxeter's book Regular polytopes. |
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May 11 |
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If $M_n(R)$ and $M_m(R)$ satisfy the same polynomial identities is it true that $m=n$? If $R$ is a ring of row-finite column finite infinite matrices, then $R\cong M_2(R)$. |
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May 11 |
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Awfully sophisticated proof for simple facts This was popular among whom? The book by Cartan and Eilenberg, the very first textbook on the subject, already has the computation done in terms of the usual very small periodic projective resolution: after that, using anything else to compute this seems pretty weird! |
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May 10 |
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A characterization of Hilbert spaces? Adding a link to the earlier question (specially if you use the notation introduced there) would be useful. |
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May 10 |
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Tenacious structure Notice that if one projectivizes $\mathbb A^d$ (with origin set at $p$) then one knows that the resulting projective space $\mathbb P^{d-1}(\mathbb F_3)$ does have a «cellular decomposition» and the question is asking if one can find one such decomposition which lifts to a decomposition of $X$ —the converse is obvious. |
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May 10 |
asked | Tenacious structure |
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May 10 |
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Functional equations Umar did not say pretty much anything, really! |
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May 9 |
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Binary Operation on a Cubic Surface (You should get the second edition) |
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May 9 |
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Binary Operation on a Cubic Surface There is a book by Manin on, more or less, this subject: Cubic forms. |
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May 5 |
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What arithmetic information is contained in the algebraic K-theory of the integers Beautiful answer! |
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May 4 |
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Can you compute the quotient set below? Your comment makes me think that you misunderstand what I wrote. I did noy say that the two polynomials $X^2$ and $X(X+1)$ are in the same orbit ---I said exactly the opposite. The rest of the comment, I don't understand it. |
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May 4 |
revised |
Can you compute the quotient set below? added 270 characters in body; added 1 characters in body |
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May 4 |
revised |
Can you compute the quotient set below? added 184 characters in body |
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May 4 |
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Can you compute the quotient set below? I did not say that you would arrive at a different problem: but the version with polynomials is expressed in terms of familiar things —polynomials and linear changes of variables— instead of weird ordered pairs under an unmotivated equivalence relation! |
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May 4 |
answered | Can you compute the quotient set below? |
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Apr 27 |
revised |
Quotients of classifying spaces added 414 characters in body |
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Apr 27 |
revised |
Quotients of classifying spaces added 48 characters in body |
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Apr 27 |
answered | Quotients of classifying spaces |
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Apr 23 |
asked | What is flexible about flexible algebras? |
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Apr 20 |
accepted | Associative algebras with Jacobson radical of codimension 1 |
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Apr 20 |
answered | Associative algebras with Jacobson radical of codimension 1 |
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Apr 15 |
revised |
The intersection complex and the Cohen-Macaulay property edited title |
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Apr 14 |
revised |
complete or open Kähler manifold and simply connected edited body; edited title |
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Apr 10 |
awarded | ● Popular Question |
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Apr 6 |
awarded | ● Nice Answer |
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Apr 2 |
awarded | ● Popular Question |
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Mar 31 |
awarded | ● Nice Question |
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Mar 31 |
revised |
The octonions on a bad day added 121 characters in body; edited body |
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Mar 31 |
asked | The octonions on a bad day |
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Mar 20 |
awarded | ● Good Answer |
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Mar 19 |
awarded | ● Popular Question |
