if we restrict to the special cases you just mentioned, doesn't same acyclicity imply equal
the first group is all torsion-free and $J$ is characterized as the set of primes at which it is uniquely divisible, the second group is all torsion and $J$ is characterized as the complement of the set of primes at which it is uniquely divisible
If $G' = \mathbb{Z}(p^\infty)$, what's the corresponding $G$? It has to be torsion and all primes $\neq p$ have to act by isomorphism, so it should be... $\mathbb{Z} / p$, but that cannot be since $\mathbb{Z} / p \otimes \mathbb{Z} / p \cong \mathbb{Z} / p$ but $\mathbb{Z}(p^\infty) \otimes \mathbb{Z} / p = 0$ (??)
@Thorgott what special case? That's a reduction!
You may assume one group is of that form, by definition
yeah, that's the first thing that came to mind as well
but how are you going to get control of the maps
hm, if you take a presentation $\bigoplus_I \mathbb{Z} \to \bigoplus_J \mathbb{Z} \to A \to 0$ and tensor with $G$, you get an exact sequence $0 \to \mathrm{Tor}(A, G) \to \bigoplus_I G \to \bigoplus_J G \to A \otimes G \to 0$, and similar for $G'$.
can we say that the middle map is an isomorphism iff it is an isomorphism in the sequence for $G'$...
Let $S$ be a compact Riemann surface and $f:S\to S$ be a continuous self map of positive degree. Is $f$ homotopic to a holomorphic map on $S$?
Motivation: I had intention to consider this question for every map $f:S\to S^2$ where $S$ is an arbitrary complex manifold. The homotopy class of a ...
i was under the impression, that a tuple is a finite ordering (a,b,c,d) but we usually refer to tensors as tuples (t_ijkl) even though no ordering seems to be given?
Fun question: Suppose we have a chess team of 6 players. Before the start of round one, we have to submit an ordered list of the players. At each round, we can send any 4 of them to play. But they have to maintain the order. So if A>B in the list then A has to be at a higher board than B( the boards are ordered as 1>2>3>4).
Now suppose A and B are our best players and also assume that before each round, we can accurately predict which 4 players of the opponent team would play. Our goal is to place A and B in the original list so that we have the most flexibility. So where should we place them?
Bousfield writes $SG$ for the Moore of type $G$ and $\Sigma X$ for the suspension of a spectrum $X$. Question for the audience: What would be the most logical choice of notation for desuspension/loops of a spectrum $X$ in this setting?
If $(X, d)$ is a metric space, then apparently it becomes a topological space if we call $U \subset X$ open when each element has an epsilon neighborhood.
But why can we be sure that each element of $X$ has such an epsilon neighborhood? Only if we can surely say this can we make the above claim.
The second and third conditions for a topological space are clear from this, I'm just asking about the first which says the empty set and $X$ itself have to be elements
Just now I saw that Laila Podlesny, Oksana Gimmel, OlegK and Cleo have all been suspended for about 100 years!! I believe they have made great contributions to the site by presenting intriguing and challenging integrals; although these were effectively sockpuppets, the intention of the person behind them wasn't bad according to me. Also, these accounts haven't been active since years. I don't see the point in suspending them for a ridiculously long period.
i don't have strong feelings about it either way, but it's now a famous example of sockpuppeting, and one point in suspending the accounts might be to avoid someone else getting caught sockpuppeting, and pointing at those and saying "when that guy did it, it was hilarious and nothing happened"
so (purely speculating here) the thinking might be, it's bad from the point of view of general site policy if looks like there's a "if you become a famous meme, it's different" exception to site rules
does it make any actual difference to those specific accounts, as you say, probably not
it wouldn't surprise me if SE staff would like to discourage someone from "doing a cleo" on other network sites, even if we wanted to have a local culture where it was permissible
$\underline{I}$ is an (ordered) collection of intervals and $\overline{\underline{I}}$ is the smallest interval containing them (plus we then remove the outmost endpoints)
sometimes I long back to the middle of the last century when this sort of notational assault was impossible due to the limitations of the humble typewriter
Let $S$ be a compact Riemann surface and $f:S\to S$ be a continuous self map of positive degree. Is $f$ homotopic to a holomorphic map on $S$?
Motivation: I had intention to consider this question for every map $f:S\to S^2$ where $S$ is an arbitrary complex manifold. The homotopy class of a ...
