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8h
comment Braid groups and the fundamental group of the configuration space of $n$ points
@SamuelReid Thought I should let you know, I've just done a major correction and update of this answer.
8h
revised Braid groups and the fundamental group of the configuration space of $n$ points
added 2521 characters in body
12h
comment One-to-one correspondance between zeta zeros and the prime powers?
I don't see where prime powers appear anywhere?
13h
comment General relationship between braid groups and mapping class groups
Anyway, why is ${\rm Homeo}^+({\cal S})$ being a ${\rm Homeo}^+({\cal S},n)$-bundle on $SF_n({\cal S})$ the correct general version of my dream? I haven't been able to mentally picture such a bundle, and I've never handled bundles before. [My intuition was that paths in configuration space "come from" paths in ${\rm Homeo}^+(\cal S)$ starting $\rm id$ that braid the $n$ points over time, hence have an endpoint in ${\rm Homeo}^+({\cal S},n)$, and when I noticed ${\rm Homeo}^+({\cal S},n)$ was a stabilizer my algebraic instinct to use orbit-stabilizer kicked in.]
13h
comment General relationship between braid groups and mapping class groups
Ah... is rotating the plane $360$ degrees not a contractible loop in ${\rm Homeo}^+(\Bbb C)$? If so, I see why that wouldn't rear its head for the closed unit disk. Thanks for the answer, and glad to know that my reasoning was (mostly) correct. BTW where do you know of Homeo groups of spheres, planes and tori from? (And does $\simeq$ mean homotopy equivalence?) I indeed have Farb checked out from the library, but just reading the first chapter I realized I should study the classification of surfaces and more hyperbolic geometry first, so that's what I've been doing a little of this summer.
1d
asked General relationship between braid groups and mapping class groups
1d
awarded  Enlightened
1d
awarded  Nice Answer
1d
comment Is the Riemann zeta function $\zeta(s)$ exactly $\pi(x)$?
This title makes no sense.
2d
revised Braid groups and the fundamental group of the configuration space of $n$ points
added 1649 characters in body
Jun
29
comment How can I prove irreducibility of polynomial over a finite field?
An irreducible polynomial can't be divided by anything except for associates (i.e. unit multiples) of itself and $1$. In particular, no polynomial can be divided by a polynomial of higher degree (you'd get a rational function). Your concept of division seems backwards. For instance, $2$ cannot be divided by $6$ (although we do say "$2$ divides $6$," notated $2\mid 6$, meaning $\exists n\in\Bbb Z:6=2n$).
Jun
29
comment On cyclic decomposition of element in $S_n$
@mathcounterexamples.net The cycle decomposition has $t_1$ $1$-cycles, $t_2$ $2$-cycles, and so on. The notation $1^{t_1}\cdots l^{t_l}$ is standard for this. The actual numbers in the decomposition are irrelevant.
Jun
26
comment Set Theory Notation: What does it mean to “\” one set with another?
By the way, division is a forward-slash, not a backwards-slash.
Jun
24
comment Solution to quadratic question of the form 0/0
Just because you can go from one equation to another doesn't mean they're equivalent.
Jun
24
comment Proof that algebraically closed fields of characteristic $p$ exist
If adding $1$ added to itself a prime number of times yields zero in the finite field $F$, then it also does so in any field $K$ containing the finite field $F$!
Jun
23
answered What does $(G:G')$ mean?
Jun
23
comment Algebraic Peter-Weyl theorem in the case of $G=SL_2$.
Can you write isotypical projectors in terms of characters and apply them to polynomials? (That's what I'd do in a finite group setting, dunno if this is available for infinite groups.) Not sure if that'd help.
Jun
23
revised Question about countable and uncountable map correspodence
deleted 288 characters in body
Jun
23
comment Algebra: operations
@Omnomnomnom Either your comment was responding to Khaled's comment, and Khaled's comment is talking about arbitrary operations, making your comment moot, or else your comment was responding to the original post, which would make your comment superfluous after mine.
Jun
23
comment Algebra: operations
Oh, are you defining E to be the inverse of e with respect to $ in your comment? @Omnomnomnom My comment was about addition and multiplication, not arbitrary operations.