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Nov
19 |
awarded | Yearling |
Nov
19 |
awarded | Yearling |
Jan
17 |
awarded | Revival |
Dec
29 |
revised |
Homological smoothness implies projectivity?
added 137 characters in body |
Dec
29 |
revised |
Homological smoothness implies projectivity?
added 1504 characters in body |
Dec
29 |
revised |
Homological smoothness implies projectivity?
added 19 characters in body |
Dec
29 |
answered | Homological smoothness implies projectivity? |
Nov
19 |
awarded | Yearling |
Nov
19 |
awarded | Yearling |
Aug
29 |
comment |
Universal Property of the Smash Product (of pointed spaces)
Akhil's answer describes a particular formalization of the idea that the smash product is characterized by: do what you expect on (stable) cells, and then glue up. If no one in a millions years would have come up with that, we are all in trouble. |
Jul
9 |
awarded | Nice Answer |
Jun
28 |
awarded | Enlightened |
Jun
28 |
awarded | Nice Answer |
Jun
27 |
awarded | Nice Answer |
Nov
20 |
awarded | Yearling |
Oct
12 |
comment |
K-theory and K-theory pushforward in topology vs. in algebraic geometry
And Remark 4.17 of op.cit., and the text around it, discusses the compatibility of that relationship with pushforwards. |
Oct
12 |
comment |
K-theory and K-theory pushforward in topology vs. in algebraic geometry
Re 1, elaborating on Daniel's comment: If you rationalize on both sides, this is asking to compare rational Chow theory with rational even-dimensional cohomology. In general, that won't go well (e.g., for $X$ a positive genus curve). It will be true only under some very restrictive hypotheses on $X$ (e.g., if $X$ is "cellular" in the sense of a locally closed decomposition by affine spaces). The result of Thomason is saying that things in fact get better if you look at higher and higher K-theory and look at torsion(/complete) instead of rationalizing. |
Sep
12 |
revised |
Constructible sheaves and dg-modules
Minor edit for clarity. |
Sep
10 |
answered | Constructible sheaves and dg-modules |
Sep
3 |
comment |
Poisson algebras as deformations vs. Poisson algebras in algebraic topology
I'm not entirely sure what you're looking for in the body of the question, but your "For example" admits a silly affirmative answer as follows. Going from chains to homology is a passage to an associated graded (for the "Postnikov filtration" $F_k V= \tau_{\geq k} V$). The $d$-Poisson algebra $H_*(\Omega^d X)$ is the associated graded of the $E_d$-algebra $C_*(\Omega^d X)$. (Here by $E_d$ I mean the operad of chains on the little $d$-disks operad. It's a filtered operad in the manner above, $C_*(\Omega^d X)$ is then a filtered algebra over this operad $E_d$, etc. etc.) |