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bio website math.mit.edu/~preygel
location MIT
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seen Aug 26 at 21:19

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.)
May
27
awarded  Editor
May
27
revised Derived categories of (coherent) sheaves of modules: exceptional images, gluing, and proper descent?
Clarifications..