6,331 reputation
152106
bio website
location
age
visits member for 4 years, 8 months
seen 3 hours ago

(formerly user "unknowngoogle", and for a very short time "red herring" but that was a red herring)


1h
awarded  Notable Question
Nov
23
reviewed Approve suggested edit on Given a Levy Exponent find the jump-measure and drift
Nov
21
comment Notion of manifold curvature?
(I mean, isn't it the usual differential/jacobian?)
Nov
21
comment Notion of manifold curvature?
What do you mean by Fréchet derivative?
Nov
21
awarded  Favorite Question
Nov
20
comment What is DAG and what has it to do with the ideas of Voevodsky?
Can we say that somehow all these notions of "geometry" are subsumed by Lurie's Higher algebra, Higher topos theory and Structured spaces (of each of which unfortunately I know nothing)?
Nov
19
comment Is true that $[\frac{\hat{A}(\mathbb HP^m)} { \hat{M}(\mathbb HP^m) }]_{4m} = 0$?
What is $p$? Is it the total Pontryagin class?
Nov
19
comment Take contraction wrt a vector field twice and define kernel mod image. Does that give anything interesting?
I haven't read the answers (yet) but it reminds me of the Koszul complex.
Nov
18
revised Take contraction wrt a vector field twice and define kernel mod image. Does that give anything interesting?
deleted 128 characters in body
Nov
18
comment Does the sequence tan(n) diverge?
Maybe you want to ask about the series $\Sigma \tan (n)$ ?
Nov
18
accepted Relation between $BG$ in topology and in algebraic geometry
Nov
18
asked Relation between $BG$ in topology and in algebraic geometry
Nov
14
comment Białynicki-Birula theory for non-complete varieties
@Dave Anderson: I found the second isomorphism on page 19 of this set of slides: mysite.science.uottawa.ca/jlema072/Borel-Moore.pdf Probably, yes, what is denoted $H^{i}_{BM}$ should be compactly supported cohomology.
Nov
13
comment Białynicki-Birula theory for non-complete varieties
My previous comment is confusing. I've just looked up in some references that for $X$ a (real) smooth manifold we have the following version of Poincaré duality: $H_{i}^{BM}(X)\cong H^{n-i}(X)$ and $H_{BM}^i(X)\cong H_{n-i}(X)$ where $n = \dim X$. So there's just a 'reflection' in the degree. Checking on the example of $\mathbb{C}^{*}$ acting on $\mathbb{C}$ I would say that, yes, BB computes BM (co)homology (with the cells of complex dimension $i$ generating degree $2i$ BM (co)homology).
Nov
13
comment Białynicki-Birula theory for non-complete varieties
@Dave Anderson: Ok, so I'm probably confusing BM homology with BM cohomology? Say we work with rational coefficients. You claim $H^{i}_{BM}(X)\cong H^{i}(X)$ whether $X$ is compact or not. On the other hand, according to the Wikipedia entry on BM homology, we would have $H_{i}^{BM}(\mathbb{C}^n)=\mathbb{Q}$ for $i=2n$ and trivial otherwise; while for ordinary homology $H_{i}(\mathbb{C}^n)=0$ (in positive degree) for the contractible space $\mathbb{C}^n$. This would suggest that in general $H_{i}^{BM}(X)\ncong H_{BM}^{i}$ as rational vector spaces?
Nov
13
revised Białynicki-Birula theory for non-complete varieties
added 509 characters in body
Nov
13
comment Białynicki-Birula theory for non-complete varieties
@Ricardo Andrade: Ok, I'll edit accordingly.
Nov
13
comment Białynicki-Birula theory for non-complete varieties
A question: when you talk about BB cells computing cohomology, do you mean singular cohomology or Borel-Moore homology (since we're on a non-compact manifold)?
Nov
13
accepted Białynicki-Birula theory for non-complete varieties
Nov
13
comment Białynicki-Birula theory for non-complete varieties
Thank you for the detailed answer!