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2d
comment Limit Group decomposition
(To clarify, my last comment refers to the current version of the question, which is fine. The original question was incomprehensible.)
2d
comment Limit Group decomposition
The question is vague because it's about a vague statement in an article. It seems fine to me, and I'm voting to reopen. (Also, I'll answer the question if it's reopened.)
Apr
18
comment The free group of a group and the kernel of a canonical morphism
@ToddTrimble, I think this answer is more useful than the question, which should probably have been closed as 'not research level'.
Apr
18
comment The free group of a group and the kernel of a canonical morphism
Since the question is trivial and this is the correct answer, I think the downvotes are quite unnecessary. +1.
Apr
12
awarded  Disciplined
Apr
12
awarded  Good Answer
Apr
8
comment finite stabilizers + compact orbit space => proper action?
This seems easy as long as the action is cellular. Presumably one can arrange this in the smooth setting.
Apr
6
comment Products of subgroups of a free group
To disambiguate, I would call $AB$ a `double coset'.
Apr
1
comment Why does this fundamental group not have elements of finite order?
It may be open in general, but there are certainly cases in which it is a theorem... (An easy example is when $X$ is a submanifold, but this hypothesis can probably be considerably relaxed.)
Mar
28
comment Obtain any 3-manifold from repeating surgeries on knots in $S^3$
@SamNead, I take your point about the base case. As for the other components of the argument - sure, they were non-trivial to spot at the time, but they're fairly standard now (as is true of many important theorems). I was really trying to address Igor's query about the gap between getting infinitely many generators and finitely many.
Mar
25
comment Decidable properties of the Cayley complex of a presentation
The list of possible 'geometric properties' is so long that this question might go on forever. But it's certainly the case that you can decide a lot of things by looking at the link $L(P)$ of the unique vertex of the presentation complex of $P$. For instance, $X(P)$ should be planar (ie embeddable in $S^2$) if and only if the cone on $L(P)$ is planar.
Mar
25
comment Normal subgroup of a totally ordered group
@YCor, yes, in the light of Dave's answer I realize that now.
Mar
23
comment Obtain any 3-manifold from repeating surgeries on knots in $S^3$
Isn't the difference between being generated by Dehn twists and being generated by finitely many Dehn twists essentially just the (obvious) statement that the action of the mapping class group on the curve complex is cocompact?
Mar
16
comment Parodies of abstruse mathematical writing
This is highly reminiscent of the exams from 1066 and all that (in another discipline).
Mar
15
comment Is there a non right-orderable torsion-free factor of the Braid group on 3 strands?
What do you mean by a factor?
Mar
15
comment uniqueness of quotients of principal congruence subgroups
So then I don't see how what you want can possibly be true. Any 2-generated finite group $Q$ will have many epimorphisms $\Gamma(2)\to Q$ (one for each generating pair), and the kernels will be different unless they differ by an automorphism of $Q$. (Unless the groups $\Gamma(2)/\Gamma(2^n)$ have the very special property that every generating pair differs by an automorphism.)
Mar
14
comment uniqueness of quotients of principal congruence subgroups
Isn't $\Gamma(2)$ (in $PSL_2(\mathbb{Z})$) a free group?
Mar
14
comment How does one justify funding for mathematics research?
One problem with this answer is that it doesn't address the point made by Campello, that mathematics funding in total accounts for a relatively tiny fraction of all science funding. Of course the odds of winning are long, but the amount being bet on a win is also pretty tiny. The examples of Euler and Gauss aren't really relevant either. Surely Turing and von Neumann are more pertinent examples.
Mar
13
comment Are all free groups linear, i.e., admit a faithful representation to GL(n,K) for some field K ?
@YCor, sorry, yes, I meant `fully residually linear of dimensions $d$'.
Mar
13
comment Are all free groups linear, i.e., admit a faithful representation to GL(n,K) for some field K ?
The fact that 'locally fully residually linear' implies linear was noticed by Tarski.