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bio website dpmms.cam.ac.uk/~hjrw2
location Cambridge
age
visits member for 5 years, 9 months
seen 13 hours ago

Jul
24
comment Automorphisms of finite order in $Out(\widehat{F_2})$
Have you thought about $\mathrm{Out}(\widehat{\mathbb{Z}})$?
Jul
24
comment dense subgroup in pro v topology
Ah right, I misunderstood you. Yes, it is true in the pro finite topology.
Jul
24
comment dense subgroup in pro v topology
Unless I misunderstood your question, this fails trvially for the profinite topology, since any subgroup of finite index is closed.
Jul
21
revised Products of elliptic isometries
Added gr.group-theory tag.
Jul
20
revised Does there exist a homotopy equivalence from $\mathbb{C}P^{2n}$ to itself that reverses orientation?
Clarified title.
Jul
20
comment Products of elliptic isometries
As Richard's answer indicates, you seem to have misinterpreted $\mathrm{Fix}_\delta$ to mean a neighbourhood of the fixed point set, whereas it should actually be the approximate fixed point set.
Jul
14
comment Cycles covering the edges of the graph corresponding to the Van Kampen diagram of a presentation of a group
I too am confused. A van Kampen diagram is a geometric proof that one element $\gamma$ of the free group on the generators $x_1,\ldots,x_n$ maps to the trivial element in $G$. It does not tell you anything about the whole of $G$. Perhaps you meant 'presentation complex'?
Jul
13
comment When to postpone a proof?
It seems to me that this question should be community-wiki. I've flagged it as such.
Jul
11
comment Categorizing finitely presented groups by complexity
You can enter your presentation into GAP or Magma and see if the group is recognized. For very small examples this will work. But you are surely aware that such a classification will become infeasibly complicated very quickly.
Jul
8
comment Your favorite papers on geometric group theory
You already mentioned three of my favourites!
Jul
1
comment Hyperbolic knot complement groups and relative dimension
No problem. Nice theorem, by the way!
Jul
1
revised Hyperbolic knot complement groups and relative dimension
Minor corrections.
Jun
30
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.