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Post AxtZBWNeCuApARiDfE by [email protected] |
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More posts by [email protected] |
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Post #AxtZBU6Cgn225lXGCG by [email protected] |
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It just struck me that while String_SU(n) follows the same pattern as String(n)… |
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Post #AxtZBUDIGQheRkqvFQ by [email protected] |
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Thus while Fivebrane structure is a 6-bundle, an SU(n)<5> structure is &q… |
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Post #AxtZBUKNq4NGnkAaIa by [email protected] |
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@highergeometer is the point that the next non-trivial homotopy group appears i… |
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Post #AxtZBUQPTfC96QzOgy by [email protected] |
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@francisbrb Yes. For Spin(n) with n≥7, π₇ is the next nontrivial homotopy … |
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Post #AxtZBUXr1z9LTWTLIO by [email protected] |
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@highergeometer So the point about Bott periodicity is that the homotopy groups… |
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Post #AxtZBUfIaJ6XqbxHto by [email protected] |
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@highergeometer What is the significance of this fact for you? |
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Post #AxtZBUkyFDdq8Cbojw by [email protected] |
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@francisbrb As noted, there's a chance to think about more explicit higher-… |
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Post #AxtZBUrLrUkIRzauga by [email protected] |
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@highergeometer a 3-crossed module sounds scary. I've been trying to just d… |
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Post #AxtZBUy5SS8KmskIBU by [email protected] |
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@francisbrb Yes, crossed squares are nice! I could also imagine something like … |
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Post #AxtZBV4762xD5ZZ6Zs by [email protected] |
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@highergeometer What about using crossed complexes. This admitedly throws away … |
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Post #AxtZBVA8jdm5OGNuyG by [email protected] |
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@francisbrb Well, yes, it might be that a crossed complex C(n) captures all/eno… |
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Post #AxtZBVFSPs1neksAG8 by [email protected] |
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@highergeometer Yes! In general I believe that there is a strictification funct… |
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Post #AxtZBVKm66HVvFMPY0 by [email protected] |
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@francisbrb Gah, why do I feel a new project brewing.... |
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Post #AxtZBVQ5mKXEBjqeps by [email protected] |
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@highergeometer Hmm, this does seem to be an interesting question. |
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Post #AxtZBVVlRF4WTKVBg0 by [email protected] |
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@francisbrb The first and biggest wrinkle that I can see is that one needs to c… |
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Post #AxtZBVduwvasscJhNw by [email protected] |
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@highergeometer that's true. I have a more basic question: if g is a semisi… |
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Post #AxtZBVjwaWPlBJ8VmK by [email protected] |
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@highergeometer Another related question. Let c in H^n(BG,Z) be one of the gene… |
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Post #AxtZBVqKCnWDV67biy by [email protected] |
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@francisbrb No, I'm not killing a higher-dim generator before a lower one. … |
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Post #AxtZBVuvvfCljOHHuK by [email protected] |
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@highergeometer I know. But what happens when you do kill a higher generator be… |
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Post #AxtZBW0baZk40yvokS by [email protected] |
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@francisbrb I don't know! I don't know any good way to do that other th… |
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Post #AxtZBW6HFUHMIZaLaa by [email protected] |
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@highergeometer couldn't you try constructing the gerbe, e.g. with Cech dat… |
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Post #AxtZBWBwuOoeaAEsQi by [email protected] |
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@francisbrb Čech data can be a bit of a nightmare if one wants a specific actu… |
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Post #AxtZBWHcZJLwrktPGq by [email protected] |
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@highergeometer Yes, that's true. I meant more of an 'in principle'… |
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Post #AxtZBWNeCuApARiDfE by [email protected] |
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@highergeometer I guess I am just saying that, abstractly and without explicitl… |
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Post #AxtZBWTfqUzhT8X23c by [email protected] |
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@francisbrb I think one can try to argue this just with the cohomology classes … |
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Post #AxtZBWa3Sm69mvW80G by [email protected] |
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@highergeometer What do you mean? In general, you could prequantize all the gen… |
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Post #AxtZBWfN90Ls3Q0NI8 by [email protected] |
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@francisbrb I guess so. One doesn't need to play around with the actual geo… |
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Post #AxtZBWlOmbAkM6pBgW by [email protected] |
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@highergeometer But I guess if you can realize these higher gerbes as crossed c… |
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Post #AxtZBWr4RVi2dhTiWe by [email protected] |
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@francisbrb Maybe! I don't know what information (if any) is contained in t… |
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Post #AxtZBWwk6QFKvI8FMm by [email protected] |
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@highergeometer Well, if you consider a dgla model for the higher Lie algebra o… |
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Post #AxtZBX23meV3BmcUee by [email protected] |
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@francisbrb Sure, but what is happening at the level of actual homotopy types, … |
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Post #AxtZBX7NSsklSH6jwW by [email protected] |
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@highergeometer Hmm, I don't know either. But it does look like I can const… |
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Post #AxtZBXCh970TilazEO by [email protected] |
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@francisbrb Nice! DM or email me more, if you want to share |
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Post #AxtZBXHeqeyby9uwy0 by [email protected] |
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@highergeometer (Hopefully there were no mistakes!) It is actually related to t… |
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Post #AxtZBXNgUFnUGqjlMO by [email protected] |
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@francisbrb Ah, ok, I wondered how you would resolve things. That method strike… |
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Post #AxtZBXU46WtwadirJ2 by [email protected] |
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@highergeometer btw, are you aware of references that use these types of resolu… |
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Post #AxtZBXZNml9er8D6au by [email protected] |
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@francisbrb I'll send a reply to your actual email ^_^ |
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Post #AxtZC8RWgvr5DToqzA by [email protected] |
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@francisbrb Well, ok. So you could have the map BG -> B^{n-1}U(1) that gives… |
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Post #AxtZCAK9hJ9D3CNzm4 by [email protected] |
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@francisbrb I was just meaning that Bott periodicity tells us that for U(n) the… |
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Post #AxtZCCJAJxXnChwEVc by [email protected] |
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@highergeometer what do the funny angular brackets mean? |
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Post #AxtZCCPXwEeFWUvKSG by [email protected] |
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@pschwahn Step in the Whitehead tower, X<n> -> X is the n-connected co… |
