David White
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Registered User
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I am a graduate student at Wesleyan University, currently in my fourth year. I study algebraic topology with Mark Hovey, and am very interested in model categories and ring spectra. I'm also getting a masters degree in computer science under Danny Krizanc, working on several random process problems, including one in particular about a certain type of random walk. My email address is dwhite03 at wesleyan dot edu
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1d |
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Drect limit of sequences A Grothendieck category has a lot of smallness (I think it's locally presentable for example) so that means Hom commutes with colimits, maybe with some hypothesis on the kind of colimit or its length. It seems your argument might hold more generally and not really need this smallness hypothesis |
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1d |
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Drect limit of sequences I thought filtered colimits always commute with finite limits. Isn't that basically what filtered colimits are good for? There's an old mathoverflow question on this subject |
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1d |
asked | Directed colimits of maps in a combinatorial model category |
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1d |
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Drect limit of sequences Your question has a large number of typos and confusing phrasing. The answer to your first question "is it true" is yes. For your second question on splittings I see no reason why splittings at each $i$ would not assemble to a splitting for $\epsilon$, but I could be wrong here. For your last question I don't understand what you're asking. You'll get better answers if you take the time to make your question clearer |
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2d |
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State of the game : cohomology of principal bundles Things have been done for finite groups. I suppose work of Bredon from the 60s is a good reference. If you start googling for equivariant cohomology you´ll come across the reference immediately; everyone cites it. For compact Lie groups check out Peter May´s work, especially the notes from the Alaska conference, which are dedicated to Gaunce Lewis iirc. More recent references will probably focus on spectra more than on spaces, so maybe will be less interesting to you. If you want to go more general than compact Lie groups then I have no idea. |
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May 17 |
answered | Waldhausen $K$-theory for $G$-spaces |
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May 16 |
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Identity on topological space but not on scheme Just so this question doesn´t hang around forever, maybe someone can post as an answer. Nadim you can even do this, just copying and pasting the comments (with attribution) and accepting your own answer. The tradition is to do this self-answer as community wiki so you don´t get reputation for someone else´s work. |
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May 15 |
accepted | Is the injective model structure on symmetric spectra Bousfield localizable? |
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May 15 |
answered | What is DAG and what has it to do with the ideas of Voevodsky? |
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May 15 |
answered | Is the injective model structure on symmetric spectra Bousfield localizable? |
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May 11 |
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Compact open topology Yep, monoidally closed |
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May 10 |
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Compact open topology It has to be functorial and satisfy the hom-tensor adjunction (sometimes called Currying). I don't think a random topology would do |
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May 10 |
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Compact open topology The reason I use the compact open topology is because it lets me view continuous maps between two spaces as a space. So it gives a function object in the category of spaces and that's what we need for it to be a monoidal category. |
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May 9 |
accepted | Diagram spectra and Algebraic Geometry |
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May 9 |
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Diagram spectra and Algebraic Geometry I didn't realize that I hadn't. I have now remedied the problem. I probably didn't accept immediately because I was hoping for more answers because my question was so broad. |
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May 9 |
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Diagram spectra and Algebraic Geometry If you want to know more about the applications of Motivic Homotopy Theory to number theory and algebraic geometry, check out my recent question and the marvellous answer I got: mathoverflow.net/questions/129762/… |
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May 9 |
answered | Diagram spectra and Algebraic Geometry |
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May 9 |
revised |
A question in category theory deleted 1 characters in body |
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May 8 |
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Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads Karol Szumilo and I have been corresponding about the issue of whether or not topological operads are admissible. I'll add an answer soon. For now, I point out that Theorem 12.2.C in Benoit Fresse's book requires an extra smallness condition in the transfer principle which Berger and Moerdijk never mention. Fresse mentions that this fails for Top, so topological operads don't form a model category (though you do get a semi model category). Because Berger-Moerdijk use the same transfer principle in their argument for admissibility, I'll bet the error is there. |
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May 6 |
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Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads Also, welcome to MathOverflow! I guess I'll be seeing you quite soon in Barcelona. Can't wait! |
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May 6 |
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Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads Thanks. I think the second mistake was the one pointed out to me. I knew it was fixed in some appendix but couldn't find it when I searched. Do you happen to know the situation for Commutative Monoids in Top? I feel like this should not form a model category, but Berger and Moerdijk clearly claim it does. If it doesn't, then that would throw doubt on Proposition 4.1 as well. Prop 4.1 is currently the only general theorem I'm aware of whose conclusion is that an operad is admissible. If there's doubt on it, that would be very sad. |
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May 6 |
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What arithmetic information is contained in the algebraic K-theory of the integers @Rebecca: Thanks, this is a great answer! I'm somewhat amazed that the Langlands program is involved with algebraic K-theory, but you explain this point very well. And that connection to Galois cohomology groups is great. Also, welcome to MathOverflow! |
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May 6 |
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What arithmetic information is contained in the algebraic K-theory of the integers Interesting. So that goes with the Iwasawa theory I guess. I'll have to look it over sometime. This is far away from the types of things I usually think about, but seems worth the effort to learn a bit. I've never heard of Catalan's constant before. Seems fascinating |
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May 6 |
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What arithmetic information is contained in the algebraic K-theory of the integers Hi Lennart. Thanks for the references, they look really cool! I guess I was being a bit sneaky trying to ask two questions at once, but I only did it because the particular talk I was thinking of when I wrote this seemed to stress that there was arithmetic information contained in both. I wouldn't be surprised if that was just because he was informally motivating things and I wouldn't be surprised to learn $K(S)$ contains no arithmetic information. I am glad to hear of this h-cobordism stuff, though. Someday I may need to motivate K-theory to a (non-algebraic) topologist |
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May 5 |
awarded | ● Nice Question |
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May 5 |
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What arithmetic information is contained in the algebraic K-theory of the integers Thanks for your answer. It seems Vandiver's Conjecture is the standard motivation for trying to understand $K_*(\mathbb{Z})$. I was mostly interested in other problems in arithmetic which could be solved by computations in $K_*(\mathbb{Z})$, so I'm going to hold off on accepting your answer because I'm hoping for more. Still, it sounds like Kurihara's paper might contain some further applications, so I'll look into that paper soon. |
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May 5 |
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What arithmetic information is contained in the algebraic K-theory of the integers Ah Peter, you know me so well. That's the perfect introduction to the subject for me. It's by one of my favorite authors and contains all of my favorite things, with just enough K-theory mixed in for me to actually learn something. Thanks for the link! By the way, now that things have settled down a bit I guess I owe you an email about those semi-model categories. It will be coming soon. |
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May 5 |
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Representing KO-theory using Clifford algebras Have you checked out the Wood reference? |
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May 5 |
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What arithmetic information is contained in the algebraic K-theory of the integers Okay, thanks. I'll have to go look into that. I've seen Teena speak and always really enjoyed it. I'll bet her writing style would also make a lot of sense. |
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May 5 |
asked | What arithmetic information is contained in the algebraic K-theory of the integers |
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May 5 |
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Localization of a pure-injective module is pure-injective? Hi Fernando. I can't remember anything about this problem, since it was so long ago. I see my links above were to wikipedia, so maybe there was some ambiguity there. A better source for info on pure injectives appears to be eprints.ma.man.ac.uk/1148/01/covered/…, and it confirms that you're right. Anyway, this hasn't been a very popular post, and I don't think the OP ever came back so I'm not going to bother trying to tweak this answer to prove $S^{-1}N$ is pure injective. I think the same methods and types of considerations should work. |
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May 4 |
accepted | Local injective model structure for simplicial presheaves |
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May 4 |
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Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads @Ricardo: Thanks for your comment. I don't mind the nitpicking at all. Do you happen to know if this model structure exists? For some reason I had it in my brain that it was impossible, but now the evidence is pointing the other way. |
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May 3 |
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Homological Algebra for Commutative Monoids? Does this also work if we replace "simplicial" by "topological"? I just posted a question which is related: mathoverflow.net/questions/129547. Page 501 of Schwede-Shipley Algebras and Modules in Monoidal Model Categories seems to be saying that for both sSet and Top you can use part (2) of their Lemma 2.3 to get a model structure. But later on the same page there's an obstacle to the existence of a model structure (albeit in a different context) related to these products of Eilenberg-Maclane spaces. If you could shed some light on this (e.g. answer the new question) I'd be very grateful |
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May 3 |
asked | Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads |
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May 3 |
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Representing KO-theory using Clifford algebras Their original paper is "Clifford Modules". A more complete discussion can be found in Wood: "Banach algebras and Bott periodicity" |
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May 3 |
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Representing KO-theory using Clifford algebras So, Hovey proved it in this course he taught, and I can go digging for the lecture notes if I remember. I don't know of a canonical reference, but I'll look. I wrote my answer the way I did to highlight the connection to Bott Periodicity, rather than getting bogged down in the details of the proof. It gets rather technical as I recall. |
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May 3 |
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Applications of Govorov-Lazard Theorem? Sure, no problem. Thanks for an interesting question |
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May 3 |
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Does anyone know where I can get a copy of Gaunce Lewis’s thesis? Thanks for your answer, and the links. I look forward to reading this, now that I have it. |
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May 2 |
accepted | Applications of Govorov-Lazard Theorem? |
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May 2 |
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Does anyone know where I can get a copy of Gaunce Lewis’s thesis? @Alex: in light of the answer below it appears that scanning it in won't be necessary. Thanks for your kind offer, though. |
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May 2 |
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Does anyone know where I can get a copy of Gaunce Lewis’s thesis? Fantastic! Thanks to Markus and Dan for providing this |
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May 2 |
asked | Does anyone know where I can get a copy of Gaunce Lewis’s thesis? |
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May 2 |
answered | Representing KO-theory using Clifford algebras |
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May 1 |
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uniqueness of $f$-localization I really like this example. I never considered this $F$ before, but it does exactly what you want. I also agree that in situations like this the condition you suggest sounds right |
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Apr 29 |
accepted | Can one make the category of pairs of topological spaces a model category? |
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Apr 29 |
answered | Can one make the category of pairs of topological spaces a model category? |
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Apr 27 |
awarded | ● Necromancer |
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Apr 18 |
answered | Applications of Govorov-Lazard Theorem? |
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Apr 18 |
awarded | ● Necromancer |
