3,711 reputation
42052
bio website math.northwestern.edu/…
location Seattle, WA
age 22
visits member for 4 years, 11 months
seen 45 mins ago
Graduate student at Northwestern. Feel free to email me at dwilson [at] u. northwestern. edu :)

13h
comment Convergence of a sum with the ranks of homotopy groups
Finite generation is a condition not a consequence of your other assumption... Edit: Ok now it is.
2d
comment Which automorphisms on $H_{1}(M^{3})$ are induced by homotopy equivalences?
I agree it should be simpler because of Mostow, but rephrasing it this way didn't seem to help me- though I didn't think about it too long. I imagine that if you run the general machine above one will find that you can rephrase the obstruction in elementary terms.
2d
comment Which automorphisms on $H_{1}(M^{3})$ are induced by homotopy equivalences?
(cont'd) so presumably someone who knows more about these manifolds could compute them. That gives you something up to p-completion, so you'll have to do something rationally as well and then glue. See, e.g., Goerss-Jardine VIII.4 for this obstruction theory spelled out, and also the work of Lannes etc.
2d
comment Which automorphisms on $H_{1}(M^{3})$ are induced by homotopy equivalences?
I don't know anything about hyperbolic 3-manifolds, but there is a general obstruction theory for lifting maps in (co)homology to actual homotopy classes of maps. The first obstruction is that the map on cohomology be a map of modules over the Steenrod algebra, but I don't think that's much of a condition in your case since 3 is a small number. After that there is a sequence of obstructions living in algebraically defined Andre-Quillen style groups in the category of unstable modules over the Steenrod algebra. That sounds very complicated and it is, but in this case there's not much to compute
May
3
comment What if homotopy were expanded to allow any connected space instead of [0,1]?
I think I'm misunderstanding something. If we're working in a world where connected=path-connected then this notion is the same as homotopy: If two maps are C-homotopic, then pick any path between the points $z_0$ and $z_1$. Precomposing with this path gives an ordinary homotopy. So is the thrust of this question just what happens if we allow weirder connected spaces?
Mar
15
comment Brandt's definition of groupoids (1926)
is one of your "groupoids" supposed to say "categories"?
Mar
10
comment How to prove that any perfect complex on an affine scheme is strictly perfect?
(and the reference for my entire comment, almost verbatim, is Thomason's classification of triangulated subcategories paper)
Mar
10
comment How to prove that any perfect complex on an affine scheme is strictly perfect?
Here's something that is true: On any scheme with an ample family of line bundles (e.g. quasi-projective, or affine, or separated regular Noetherian) every perfect complex is quasi-isomorphic to a strictly perfect complex. I'm not sure if that's what you meant by "is" in your claim, but the reference is SGA6 II.2.2.8 or Thomason-Trobaugh 2.3.1.
Mar
7
comment Lemma 2.1.1.4 in Lurie's HTT
For the first question: I believe the exact thing I need is the aforementioned corollary or 2.1.2.10, I can try to rewrite this more clearly later.
Mar
7
comment Lemma 2.1.1.4 in Lurie's HTT
For your second question: Applying the last argument for $Y = K$ and $Y = X_s$ shows that in both cases the homotopy class of a lift is determined by $f$, i.e. there is only one homotopy class of lift for $K \times \Delta^1 \rightarrow S$ so it must be the one obtained by composiiton.
Mar
7
comment Lemma 2.1.1.4 in Lurie's HTT
(Alternatively I can quote Corollary 2.1.2.9 of HTT if you don't like that argument at the end.)
Mar
7
answered Lemma 2.1.1.4 in Lurie's HTT
Feb
10
comment Anything between vector bundles and sphere bundles?
I thing taking connective covers moves the wrong way. For example, we have a map $BO \rightarrow BhAut(S)$. What you're trying to do (stably) is factor this map through other things. A connective cover, say $SO$, gives a map $BSO \rightarrow BO$ which is not what you want.
Feb
9
awarded  Popular Question
Feb
8
awarded  Nice Question
Feb
8
accepted Mazur secret Bourbaki report “Analyse p-adique”
Feb
8
comment Mazur secret Bourbaki report “Analyse p-adique”
This is awesome! Thanks for your heroic dedication to the spread of knowledge! Hope the physicists didn't burn down your office though...
Feb
8
awarded  Inquisitive
Feb
7
comment Mazur secret Bourbaki report “Analyse p-adique”
Apparently it's been too long since I've asked a question and I've forgotten where to find the "Community Wiki" option... Help?
Feb
7
asked Mazur secret Bourbaki report “Analyse p-adique”