some guy on the street
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Registered User
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May 9 |
awarded | ● Nice Question |
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May 9 |
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Discrete disjoint covering of integer lattices I think that's what I was trying to say... but I'd have quibbled $\Sigma a_{ij} v_j$; and now I'm convinced that there are always exactly $n$ such $[a_{i\dot}]$; and so the interest is in how might this fail to give a basis for $\mathbb{Z}^n$... I'm now convinced this gives a list of all solutions in every case; I still like that Kevin's answer gives a specific solution in all dimensions, which is closer to what I was wondering about, but this is really nifty! |
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May 9 |
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Discrete disjoint covering of integer lattices could you explain the "$\Sigma a_i v_i=u_i"? I can see that there are finitely many HNFs to check, and that they're enough... are we basically trying to see if the cube spanned by an HNF contains enough independent integer points? |
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May 9 |
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Discrete disjoint covering of integer lattices And it turns out that the Cartan matrix for $A_n$ is always a solution; this explains the bases already in the $n=1,2$ case; the haphazard found base for $n=3$ I suspect has the noncyclic group of order $4$ as quotient. |
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May 9 |
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Discrete disjoint covering of integer lattices I also want to say that this really is quite beautiful. Thanks! |
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May 9 |
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Discrete disjoint covering of integer lattices OK, I think I believe you, but let me check this... |
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May 8 |
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Discrete disjoint covering of integer lattices or else I could have omited "translates of" |
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May 8 |
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Discrete disjoint covering of integer lattices The intent is, pick one such simplex, and cover $Z^n$ with translates of that. |
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May 8 |
revised |
Discrete disjoint covering of integer lattices replace idiosyncratic terminology |
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May 8 |
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Discrete disjoint covering of integer lattices @Gerry, Ben has it right; I should have said "minimal $n$-simplex", because they're all $SL_n$-the same... in fact, I think I will. |
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May 7 |
asked | Discrete disjoint covering of integer lattices |
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Apr 23 |
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Stratifications and Cohomology Computations I think you are looking for Spectral Sequences (which thought makes me feel somewhat gloomy...) on which there is a thorough reference by McCleary. Good luck to you! |
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Apr 2 |
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bar-cobar or cobar-bar ahem, [nlab entry](ncatlab.org/nlab/show/bar+and+cobar+construction) |
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Apr 2 |
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bar-cobar or cobar-bar ... are you wanting to update the nLab entry? or is it something else? |
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Apr 1 |
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When can you desuspend a homotopy cogroup? all spaces are $A_1$; H means $A_2$; $A_n$ is the playground Stasheff built, and where associahedra are from; he constructs a family of $H$ spaces that are $A_p$ but not $A_{p+1}$ for many (I think prime?) values of $p$ (or $p+1$, perhaps... this paper is sitting in my computer, why don't I look it up?!) Anyways, Stasheff, Transactions AMS Vol 108 No.2 pp 275-292 |
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Jan 22 |
awarded | ● Nice Answer |
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Dec 31 |
awarded | ● Popular Question |
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Dec 19 |
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Status of the Isomorphism problem for automatic groups? @André, you know, I mean it feels a bit like cheating... |
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Dec 19 |
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Status of the Isomorphism problem for automatic groups? @Jim: what I mean is, this is the sort of picky question that I'm sure, if settled, was only done recently and I furthermore don't know who would write about it, nor what keywords to put into mathscinet/arxiv/google scholar search etc. Eight years ago or so my first move would have been to ask Dani Wise, just because he taught me about Gromov hyperbolic groups and the Rips complex, but he's not handy right now and I can't get to a library. |
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Dec 17 |
asked | Status of the Isomorphism problem for automatic groups? |
