Reputation
4,506
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
18 44
Impact
~87k people reached

Apr
2
answered Long exact sequence of homotopy groups $\pi_n$ for a pointed homotopy pullback square
Mar
4
awarded  Notable Question
Feb
25
awarded  Nice Question
Feb
5
awarded  Enlightened
Feb
5
awarded  Nice Answer
Nov
25
awarded  Notable Question
Nov
13
awarded  Pundit
Sep
27
awarded  Yearling
Sep
16
awarded  Nice Answer
Aug
17
comment Topological Boundary Map
Here's something that might be helpful for context. Given a (homotopy) cofiber sequence $A \to X \to X/A$ (say of based spaces), you can "rotate" this to a new cofiber sequence $X \to X/A \to \Sigma A$, and this procedure can be iterated indefinitely. An immediate consequence of this Corollary is that all the resulting long exact sequences in $E$-homology are all canonically isomorphic (up to degree shifts -- things get skewed once per rotation).
Aug
16
comment Why steenrod commute with transgression
Hi @rj7k8 -- it's been ages since I've thought about this stuff (and it looks like my reference to pp. 106-7 of May's Concise Course were actually off, at least compared to the edition I'm looking at now). But I would expect that this might come from the cofiber sequences defining the attaching maps for your CW-complex (along with an understanding of the behavior of your chosen homology theory on spheres and disks). If you give me a more precise reference to what you're confused about, I'd be happy to see if I can say more.
Aug
14
awarded  Revival
Jun
8
comment What are $E_\infty$-rings?
@user43687 Ah, okay. Well, either Lurie's thesis or, in a slightly different direction, his ICM address (which discusses deformation theory in the derived context) would be a great place to start in that case.
Jun
8
comment What are $E_\infty$-rings?
@user43687 I don't think I've ever really written anything down about operads. My own understanding of them has come bit by bit, cobbled together from a number of different contexts. Can you be more specific about something that you don't yet understand but would like to?
Mar
27
comment What's the point of spectra?
@DmitriPavlov Interesting, thanks for pointing that out!
Mar
4
awarded  Good Answer
Jan
31
awarded  Nice Question
Jan
12
awarded  Good Answer
Oct
31
awarded  Popular Question
Sep
30
awarded  Explainer