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bio website math.berkeley.edu/~ianagol
location Berkeley
age 44
visits member for 4 years, 10 months
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I'm a professor at UC Berkeley working predominantly in the field of low-dimensional topology.


2d
awarded  Nice Answer
2d
comment When is the profinite completion a pro-$p$ group?
@YiftachBarnea: do you have a nice example of a non-torsion finitely generated pro-p group which has finite abelianization (i.e. no map to $\mathbb{Z}_p$), and say which isn't powerful? I think Lazards result should rule out groups with powerful pro-p completion.
Aug
26
comment When is the profinite completion a pro-$p$ group?
The basilica group appears to have infinite abelianization.
Aug
26
comment When is the profinite completion a pro-$p$ group?
Actually, I thought about this a bit more, and I don't see any way to guarantee that the RF quotient is non-torsion.
Aug
26
answered When is the profinite completion a pro-$p$ group?
Aug
22
comment How to find ICM talks?
I've made a version of my contribution to the ICM available here: math.berkeley.edu/sites/default/files/faculty/files/…
Aug
21
comment Heegaard genera of arithmetic 3-manifolds
Yes, usually an arithmetic manifold is defined up to commensurability, so may include non congruence lattices. If Neil intended the meaning in Gromov-Guth, then he should probably clarify, since it is nonstandard.
Aug
20
comment Heegaard genera of arithmetic 3-manifolds
Their argument only applies to congruence arithmetic manifolds.
Aug
20
answered Heegaard genera of arithmetic 3-manifolds
Aug
6
comment Faithful representations of free pro-p groups
You might have a look at "Analytic pro-p groups": books.google.com/books?id=Fjq-ngEACAAJ Since $F(p,m)$ is compact, the image must lie in a compact subgroup of $GL(n,F)$, which (up to finite index) is conjugate into $GL(n,\mathbb{O}_F)$. As shown in the book, such groups are "p-powerful", which in particular implies that they are analytic and not free.
Jul
29
revised Are there any very hard unknots?
added 14 characters in body
Jul
27
comment Reference for the result that the systol map from Teichmuller space to curve complex is coarsely Lipschitz
This follows immediately from the main result (Theorem 1.1) of this paper, although I think it was known before by Minsky: link.springer.com/article/10.1007%2Fs00039-007-0615-x
Jul
27
answered Properties of the Burnside kernel
Jul
24
comment Borel-Serre compactification of $\mathbb{H}^3 / SL_2(\mathcal{O}_K)$
There's a minor correction: for $K=\mathbb{Q}[\sqrt{-1}], \mathbb{Q}[\sqrt{-3}]$, the cusp is actually an orbifold quotient of the elliptic curve by the group of units.
Jul
22
comment Are there infinitely many commensurable classes of finite-covolume hyperbolic Coxeter groups?
@HaoCHEN: I see, yes, this is similar to the technique of Gromov-Piatetskii-Shapiro I was alluding to. I wasn't aware of these examples (even though I downloaded a copy of Vinberg's paper :).
Jul
22
comment Fake versus Exotic
The formula near the end of the paper looks reminiscent of a formula for geodesic torsion (but missing a $\cos(\phi_i)$ factor). Since the geodesic torsion of a curve of intersection of surfaces intersecting at constant angle is the same, I think this reproves your formula (maybe with a $\cos(\phi_i)$ factor or using $\sin(2\phi_i)$ instead)? encyclopediaofmath.org/index.php/Geodesic_torsion
Jul
22
awarded  Enlightened
Jul
22
awarded  Nice Answer
Jul
20
comment A question on involutions on the Lie algebra of vector fields
On odd dimensional spheres, the antipodal map works.
Jul
20
comment A question on involutions on the Lie algebra of vector fields
What do you have in mind for the Killing form for the space of vector fields?