Andy Putman
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Registered User
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associate professor at Rice University
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May 14 |
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Research on the structure of a non-Goldbach number? Questions about whether anything is known about a very specific topic are fine, but the topic in question has to be much more specific and better thought out than your question. |
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May 14 |
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Research on the structure of a non-Goldbach number? This is far too vague for MO. |
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May 12 |
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Mapping class group of once-punctured torus @Misha : Ah, so that's the statement you are after! I had assumed that you wanted a reference for the fact that the Birman exact sequence becomes an isomorphism for a once-punctured torus. I don't think I've ever seen the statement you want in print, though of course everyone (suitably interpreted) knows it. My inclination would just be to do as you suggest and say that it is well-known and easy to prove. |
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May 12 |
answered | Mapping class group of once-punctured torus |
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May 12 |
accepted | Generators of sections of free groups |
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May 11 |
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The role of the Automatic Groups in the history of Geometric Group Theory @Misha : I largely agree with you on the significance of automatic group theory within geometric group theory. But they do have a few triumphs. For instance, I know of no proof that mapping class groups have quadratic isoperimetric inequalities that does not use Mosher's theorem they they are automatic (or at least its proof). |
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May 10 |
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The role of the Automatic Groups in the history of Geometric Group Theory I think that lots of people know about automatic groups; certainly I spent lots of time with ECHLPT in grad school. But the remaining open questions are really hard, so not too many people are actively working on them. That happens to a lot of subjects. Eventually someone will come along with a big idea and the subject will start moving again... |
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May 10 |
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Generators of sections of free groups It's nontrivial to compute it, but there is a huge literature on group cohomology, so there are many tools available. To help your search, you should be aware that $H_2(G;\mathbb{Z})$ is also known as the Schur multiplier of $G$. For a particular finite group of reasonable size, by the way, you should be able to compute $H_2$ using GAP. The relevant packages are cohomolo (see gap-system.org/Packages/cohomolo.html) and hap (see gap-system.org/Packages/hap.html). |
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May 9 |
answered | Generators of sections of free groups |
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May 7 |
awarded | ● Enlightened |
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May 7 |
awarded | ● Nice Answer |
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May 6 |
accepted | When does an even-dimensional manifold fiber over an odd-dimensional manifold? |
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May 5 |
answered | When does an even-dimensional manifold fiber over an odd-dimensional manifold? |
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May 1 |
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“Motivic structure on higher homotopy of non-nilpotent spaces” ? Deepam is currently a postdoc at VU Amsterdam. I believe that his email address is deeppatel1981@gmail.com. |
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Apr 29 |
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Importants topics, research sites for algorithms, algebric geometry If you are an undergraduate computer science major, then it is very unlikely that you will be able to decode the research literature in algebraic geometry. I suggest speaking to professors at your university for advice. In any case, this question is off-topic for MO, so I have voted to close. |
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Apr 29 |
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Grothendieck 's question - any update? If all you want is an exposition of Serre's theorem, then David Speyer wrote up a nice account on the Secret Blogging Seminar : sbseminar.wordpress.com/2009/07/28/… |
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Apr 27 |
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Reference for Rationality in Algebraic Groups in the Language of Schemes? They're not yet complete, so I don't know if they will eventually have everything you want, but Milne is in the process of writing a long book on algebraic groups from the perspective of group schemes. My impression is that he wants to do the stuff that Borel does (+ more) from a modern perspective. What's written is here : jmilne.org/math/CourseNotes/ala.html |
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Apr 26 |
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Classification of groups in which the centralizer of every non-identity element is cyclic @solovei : People would have reacted better if you had done two things. First, you should have phrased it as a question rather than as an imperative; as it was written, it "sounded" like homework. Second, you should have written a bit more. I'm fine with relatively terse questions, but this question needed more discussion than you gave. By the way, I voted to reopen. |
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Apr 26 |
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Classification of groups in which the centralizer of every non-identity element is cyclic (the answer I gave is for finite groups. as Misha indicated, it is hopeless to answer it for infinite groups). |
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Apr 26 |
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Classification of groups in which the centralizer of every non-identity element is cyclic (comment about this being hw deleted, I realized that it is a little harder than I thought). This is answered in Theorem 10 of the following paper : rose-hulman.edu/math/MSTR/MSTRpubs/1991/… |
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Apr 10 |
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Would Euler’s proofs get published in a modern math Journal, especially considering his treatment of the Infinite? I'm very late to this party, but I think it is important to point out that Thurston had complete and rigorous proofs of all the results he claimed. He discussed them with many people, and whenever pressed was able to produce as many details as people needed. He just chose not to write papers containing all the details of his proofs. The paper that Greg Graviton refers to contains his justification for this decision. |
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Apr 6 |
awarded | ● Nice Answer |
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Apr 4 |
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Homotopy equvalence from contractibility of fiber. Properness is certainly needed; it is not hard to construct counterexamples without it. I do not know whether assuming that $f$ is cellular is good enough. |
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Apr 4 |
accepted | Homotopy equvalence from contractibility of fiber. |
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Apr 4 |
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Homotopy equvalence from contractibility of fiber. @Vel Nias : It depends on your conventions. All right-thinking people consider the empty set non-connected (and certainly not contractible), but just in case the OP has other ideas I thought I'd avoid this issue by assuming surjectivity. |
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Apr 4 |
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The existence of meromorphic functions on Riemann surfaces I was thinking of his "Lectures on Riemann Surfaces". However, looking at it now (I wasn't in my office when I wrote that), the proof I had in mind is not there. So look at the book of Narasimhan on compact Riemann surfaces; the proof is towards the end of the chapter on finiteness theorems. |
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Apr 3 |
answered | Homotopy equvalence from contractibility of fiber. |
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Apr 1 |
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Stable commutator length of elements in free groups. I think that $\text{scl}(g)$ (for "stable commutator length of $g$) is pretty standard at this point. |
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Apr 1 |
awarded | ● Nice Answer |
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Apr 1 |
awarded | ● Nice Answer |
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Mar 30 |
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The existence of meromorphic functions on Riemann surfaces I think that it's much easier than uniformization. The proof I'm thinking of is the one in Gunning's book and Narasimhan's book (and many others). The heart of it is showing that for any holomorphic line bundle $L$, the vector spaces $H^0(S,L)$ and $H^1(S,L)$ are finite-dimensional. This requires some functional analysis, but nothing all that deep. |
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Mar 24 |
awarded | ● Popular Question |
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Mar 23 |
awarded | ● Nice Answer |
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Mar 23 |
awarded | ● Nice Answer |
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Mar 21 |
awarded | ● Cleanup |
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Mar 21 |
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Is connected correlation/cumulant expansion additive? Please do not deface your question like that. I rolled back your revisions. |
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Mar 20 |
awarded | ● Enlightened |
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Mar 20 |
awarded | ● Enlightened |
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Mar 20 |
awarded | ● Nice Answer |
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Mar 20 |
awarded | ● Nice Answer |
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Mar 19 |
awarded | ● Enlightened |
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Mar 19 |
awarded | ● Enlightened |
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Mar 19 |
awarded | ● Nice Answer |
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Mar 19 |
awarded | ● Nice Answer |
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Mar 18 |
awarded | ● Enlightened |
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Mar 18 |
awarded | ● Enlightened |
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Mar 18 |
awarded | ● Nice Answer |
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Mar 18 |
awarded | ● Nice Answer |
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Mar 13 |
awarded | ● Good Question |
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Mar 12 |
revised |
Which manifolds are homeomorphic to simplicial complexes? added 254 characters in body |
