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bio website dpmms.cam.ac.uk/~hjrw2
location Cambridge
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visits member for 5 years, 8 months
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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 non-identity 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 non-identity element is cyclic
In fact, Rips found (torsion-free) 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 word-hyperbolic. A (torsion-free) counterexample was found by Noel Brady. I think the correct statement is now 'For torsion-free 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 pro-p dense subgroup in the free group
Added gr.group-theory 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 "well-behaved"'. 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 community-wiki.
Jun
15
comment pro-p 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 Perron--Frobenius 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 (Lucas-Penrose 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 'h-principle', 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.group-theory tag.
May
20
revised Which L-functions are not “Langlands-Shahidi L-functions”?
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.