bio  website  dpmms.cam.ac.uk/~hjrw2 

location  Cambridge  
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visits  member for  5 years, 5 months 
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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 
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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 
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Products of subgroups of a free group
To disambiguate, I would call $AB$ a `double coset'. 
Apr 1 
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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 
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Obtain any 3manifold 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 nontrivial 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 
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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 
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Normal subgroup of a totally ordered group
@YCor, yes, in the light of Dave's answer I realize that now. 
Mar 23 
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Obtain any 3manifold 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 
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Parodies of abstruse mathematical writing
This is highly reminiscent of the exams from 1066 and all that (in another discipline). 
Mar 15 
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Is there a non rightorderable torsionfree factor of the Braid group on 3 strands?
What do you mean by a factor? 
Mar 15 
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uniqueness of quotients of principal congruence subgroups
So then I don't see how what you want can possibly be true. Any 2generated 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 
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uniqueness of quotients of principal congruence subgroups
Isn't $\Gamma(2)$ (in $PSL_2(\mathbb{Z})$) a free group? 
Mar 14 
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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 
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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 
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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. 