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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...
May
18
comment differential in AHSS for spin cobordism
Well, for any cohomology theory the first non-trivial differential in AHSS ($d_2$ for MSpin, $d_3$ for BU...) is a stable cohomological operation. All cohomological operations are known and in low degree there are very few choices. In particular, there is only one non-trivial operation of deg 2 with Z/2-coefficients, $Sq^2$.
May
18
comment Proof that the subalgebra generated by any two elements of $\mathbb{O}$ is isomorphic to $\mathbb{R}$, $\mathbb{C}$, or $\mathbb{H}$
...that was the plan I had in mind — but actually, proving 'diassociativity' seems to be not that easy, sorry.
May
18
comment Proof that the subalgebra generated by any two elements of $\mathbb{O}$ is isomorphic to $\mathbb{R}$, $\mathbb{C}$, or $\mathbb{H}$
Indeed. Using a similar argument one can show that any associative division algebra is $\mathbb R$, $\mathbb C$ or $\mathbb H$. So if we can show the well-known fact that a subalgebra of $\mathbb O$ is associative, we're done...
May
18
comment Proof that the subalgebra generated by any two elements of $\mathbb{O}$ is isomorphic to $\mathbb{R}$, $\mathbb{C}$, or $\mathbb{H}$
Can you prove that a subalgebra of $\mathbb H$ generated by any non-real element is isomorphic to $\mathbb C$?
May
18
comment differential in AHSS for spin cobordism
(Re: Is this also the case here?) Sure — but one still needs to show that this operation is nonzero...
May
17
comment Determining if these surjections have sections
I wonder if $\pi^{-1}(A_5)$ is always isomorphic to the binary icosahedral group (and not to $S_5$)...