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May
27
comment Prove $\sum_{n= -\infty}^{\infty} \frac{1}{(t+n)^2} = \frac{\pi^2 }{\sin^2(\pi t)}$ using f(x)=1-|x| and Poisson summation formula
Related: Showing $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2}=\frac{\pi^2}{\sin^2(\pi z)}$ & $\sum\limits_{k = - \infty }^\infty {\frac{{{{\left( { - 1} \right)}^k}}}{{a + k}} = \frac{\pi }{{\sin \pi a}}} $
May
27
comment Spin manifold and the second Stiefel-Whitney class
@QiaochuYuan Sure (the only difference is the first sentences, essentially ;-)
May
26
comment Spin manifold and the second Stiefel-Whitney class
Related: Which manifolds are parallelizable?
May
25
comment Can one prove the existence of tensor product without explicitly constructing it?
Related: Existence proof of the tensor product using the Adjoint functor theorem
May
25
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
Related: Contour approach to Riemann zeta functional equation
May
25
comment There does not exist a map $S^2\times S^2\to \mathbb{CP}^2$ with odd degree.
Related: Minimal Degree of map $S^2\times S^2\to \mathbb{CP}^2$
May
25
comment Minimal Degree of map $S^2\times S^2\mapsto \mathbb{CP}^2$
In the same vein: $[S^2\times S^2,\mathbb CP^2]=[S^2\times S^2,\mathbb CP^\infty]=H^2(S^2\times S^2)$ — i.e. all values of $(h,k)$ are attained.
May
24
comment Notation and shorthand of cobordism G=O, SO, U
Orthogonal / Special orthogonal / unitary (as in Lie group names).
May
23
comment Intuition of higher push-forward constant sheaves.
If $Y=\text{pt}$, $R^if_*E=H^i(X;E)$. In general, derived push-forward $\cong$ fiberwise cohomology.
May
22
comment Simpler zeta zeros
Ah, I understand the question now. This looks somewhat similar to, say, exponential regularization of (divergent) series, so maybe it has some meaning...
May
22
comment Simpler zeta zeros
$\sum n^{-s}$ diverges when $\operatorname{Re}s<1$ (in particular, when $s=1/2+iy$). So, no, you have to use reflection formula or something like that to define $\zeta(s)$ in the 'interesting' area.
May
22
comment extension problem of a spectral sequence
It means that there is a filtration on $H_n(X)$ s.t. the factor of two adjacent terms is $E_{p,n-p}^\infty$ (so e.g. $E_{1,0}=\mathbb Z/2=E_{0,1}$ can correspond to $H_1$ either $\mathbb Z/2\oplus\mathbb Z/2$ or $\mathbb Z/4$).
May
22
comment how to prove Euler Characteristic of cw complex $\chi(X)=\chi (A)+\chi (B)-\chi (A \cap B)$.
Well, can you indeed? If unsure, consider some examples first...
May
22
comment how to prove Euler Characteristic of cw complex $\chi(X)=\chi (A)+\chi (B)-\chi (A \cap B)$.
Great. Do you know any theorem linking together H(X), H(A), H(B) and H(intersection)?..
May
22
comment how to prove Euler Characteristic of cw complex $\chi(X)=\chi (A)+\chi (B)-\chi (A \cap B)$.
What is your definition of $\chi$?
May
21
comment Open covers by simply connected sets and fundamental group
@Daniel, OP — oh, I'm sorry, I misread the question
May
20
comment Reference request for Rothenberg Steenrod Spectral Sequence
@draks... I guess, neil-strickland.staff.shef.ac.uk/courses/bestiary/ss.pdf
May
18
comment differential in AHSS for spin cobordism
Oh, my wording was not clear perhaps: one need to show that (not $Sq^2$ but) the operation $d_2$ is non-zero — than it coincides with the only non-zero operation of corresp. deg., $Sq^2$.
May
18
comment differential in AHSS for spin cobordism
...BTW could you please point out where exactly att. notes show that $d_2$ is non-trivial?
May
18
comment differential in AHSS for spin cobordism
...Higher differentials, on the other hand, are not coh. operations but higher coh. operations (secondary etc) — which are much less... tractable. (That's just my ignorance, but) I don't know if there is an explicit description even for $d_5$ in AHSS for complex K-theory...