4,136 reputation
42354
bio website math.northwestern.edu/…
location Seattle, WA
age 22
visits member for 5 years, 1 month
seen 3 hours ago
Graduate student at Northwestern. Feel free to email me at dwilson [at] u. northwestern. edu :)

15h
comment cohomology ring of cross-section space of one-point compactification of tangent bundle
I think your best bet is computing this using nonabelian Poincaré duality (at least if you're willing to stick with compact manifolds or compactly supported sections). A good reference is arxiv.org/pdf/1206.5522v4.pdf
1d
comment Is a pullback along a Dold fibration a homotopy pullback?
The link doesn't seem to work on the app (for me), but here's the paper: math.uiuc.edu/~rezk/rezk-sharp-maps.pdf
1d
answered Is a pullback along a Dold fibration a homotopy pullback?
Aug
1
answered Reference for (co)limit-preserving functor $X\mapsto R^X$
Jul
28
awarded  Nice Answer
Jul
28
answered Is there a generalization of homotopy groups to fractional dimensions
Jul
27
comment Is there a generalization of homotopy groups to fractional dimensions
also: if $X$ is a G-space you can stick in representation spheres for $*$, and if $X$ is a motivic space you can stick in two different types of integers into the $*$ spot- one corresponding to the ordinary sphere, and the other to $\mathbb{G}_m$.
Jul
27
comment Is there a generalization of homotopy groups to fractional dimensions
People are fond, nowadays, of interpreting the $*$ is $\pi_*$ to be pretty general elements of the Picard group of whatever category you're in. For arbitrary spaces, there's just the integer grading. However, if you're space is K(1)-local then you get at least a $p$-adics worth of numbers to stick in the $*$ slot. (So if $p \ne 2$ you get a $\pi_{1/2}$). Cf. [Hopkins, Mahowald, Sadofsky] and more recent work Hovey, Goerss, Henn, Rezk, etc. for higher chromatic analogues
Jul
19
comment What do formal group laws of height $\geq 3$ look like?
I feel out of the loop. Can someone explain what exactly these are pictures of? (I know what a FGL is, just not how to interpret dots on the screen...)
Jul
19
comment Quasicategorical Construction of a Cosimplicial Map of Rognes
Don't have anything useful, but: (1) this looks like a shearing map showing something or other is a torsor. I vaguely remember similar things appearing in the Galois descent part of DAG XI. Of course Luries notion of étale is more restrictive but maybe this diagram appears. (2) when dealing with cosimplicial objects in infty categories you can build maps in a pretty straightforward way that's not too far from classical category theory-see the appendix of HTT when he talks about reedy categories
Jul
15
comment Stabilization of a generic pointed model category
There is no problem with 1.4.2.24 of Higher Algebra. The condition in the statement requires that $\mathcal{C}$ be pointed and have finite limits, which is a property clearly independent of the universe you're in.
Jul
10
comment Why do we need filtered categories to index ind-objects?
French, but math french isn't difficult
Jul
10
answered Why do we need filtered categories to index ind-objects?
Jun
29
comment On combinatorial and cellular model categories and infinity categories
A.5 here: hopf.math.purdue.edu/Dugger/smod.pdf
Jun
27
awarded  Necromancer
Jun
21
awarded  Yearling
Jun
20
comment On combinatorial and cellular model categories and infinity categories
And I'll add the reference when I get back- about to board a plane :)
Jun
20
comment On combinatorial and cellular model categories and infinity categories
Pro-categories are examples of opposites of presentable things... Indeed: something is accessible if and only if it is "Ind" on a small category, so pro guys are precisely the opposites of accessible categories. When the small category you started with has finite (co)limits then you get presentable categories and their opposites for Ind and Pro.
Jun
20
answered On combinatorial and cellular model categories and infinity categories
Jun
19
comment If a topological space has vanishing $n$th homology for every possible homology theory, does it have vanishing $n$th homotopy?
To answer your last question, knowing about what all cohomology theories say about a space is the same as knowing its stable homotopy type. So you're asking "Are there good references for stable homotopy theory?" and the answer to that question is "Yes" :)