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

location  Cambridge  
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visits  member for  5 years, 8 months 
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48m

answered  Hyperbolic knot complement groups and relative dimension 
Jun 27 
awarded  Good Answer 
Jun 26 
comment 
Classification of groups in which the centralizer of every nonidentity element is cyclic
PS Ian, I know you know this. But I thought it worth setting the record straight. 
Jun 26 
comment 
Classification of groups in which the centralizer of every nonidentity element is cyclic
In fact, Rips found (torsionfree) examples of finitely generated but infinitely presented (and hence not hyperbolic) subgroups of hyperbolic groups in the early '80s. I think Gromov may have asked whether every such finitely presented group is wordhyperbolic. A (torsionfree) counterexample was found by Noel Brady. I think the correct statement is now 'For torsionfree group of type $F_3$, your question is as difficult as Gromov's question.' 
Jun 23 
revised 
Abelianization of limit groups
Added Weidmann's proof that $G$ has rank four. 
Jun 22 
comment 
Abelianization of limit groups
I mean, look at the papers authored (independently) by Louder and Weidmann. For instance: R. Weidmann, 'The Nielsen method for groups acting on trees'. Proc. London Math. Soc. (3) 85 (2002), no. 1, 93–118; or L. Louder, 'Scott complexity and adjoining roots to finitely generated groups', Groups Geom. Dyn. 7 (2013), no. 2, 451–474. 
Jun 22 
answered  Abelianization of limit groups 
Jun 19 
revised 
prop dense subgroup in the free group
Added gr.grouptheory tag. 
Jun 19 
revised 
Compact open topology on $\mathrm{Homeo}(X)$
Removed unnecessary latex used only for emphasis. 
Jun 18 
comment 
Transitivity on $\mathbb{N}_0$ — a 42 problem
Can you be a bit more precise about your assertion that 'A positive answer would mean that groups generated by 3 class transpositions are "wellbehaved"'. Perhaps one could disprove the conjecture by exhibiting undecidability phenomena among these groups? 
Jun 18 
comment 
Combinatorial results by Poincaré duality
Since this question doesn't have a unique correct answer, I'm going to flag it for communitywiki. 
Jun 15 
comment 
prop topology on a free group
At the risk of asking the obvious, have you tried looking in Howie's paper? 
Jun 6 
comment 
Solving algebraic problems with topology
And, more generally, the entire PerronFrobenius theorem can be deduced from Banach's contraction mapping theorem, using the Hilbert metric on the positive orthant. 
Jun 4 
comment 
when are local quasigeodesics global in CAT(0)
@IgorRivin, thanks! 
Jun 3 
comment 
when are local quasigeodesics global in CAT(0)
What's the counterexample in the Euclidean plane? It's well known that global quasigeodesics there need not be uniformly close to a geodesic, but that's not quite the same thing... 
May 27 
comment 
What exactly is wrong with this statement (LucasPenrose fallacy)?
This is a famous philosophical fallacy. It's a good question, but not suitable for MO, so I too will vote to close. In case it helps, I seem to remember that the fallacy is discussed in Goedel, Escher, Bach, and also in one of Daniel Dennett's popular books (perhaps Darwin's Dangerous Idea?). 
May 26 
comment 
John Nash's Mathematical Legacy
@WillieWong, as someone who has often heard the term 'hprinciple', but didn't know that it was inspired by Nash (among others), I'm very glad you mentioned it! 
May 25 
revised 
Number of trivializations of a trivial word in the free group
Added gr.grouptheory tag. 
May 20 
revised 
Which Lfunctions are not “LanglandsShahidi Lfunctions”?
Corrected link text. 
May 15 
comment 
Splitting over infinite generated abelian subgroup?
Well, for instance, any quasiconvex subgroup of infinite index in a hyperbolic group is contained in an infinitely generated subgroup. 