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bio website math.berkeley.edu/~ianagol
location Berkeley
age 44
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I'm a professor at UC Berkeley working predominantly in the field of low-dimensional topology.


59m
revised Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?
added 70 characters in body
1h
answered Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?
Dec
10
awarded  Good Answer
Dec
10
comment Fundamental groups and homology groups of closed subsets of the plane
See this question: mathoverflow.net/q/189323/1345
Dec
10
awarded  Nice Answer
Dec
9
answered Can a subset of the plane have nontrivial $H_2$ or $\pi_2$?
Dec
8
awarded  Good Answer
Nov
23
answered Koebe–Andreev–Thurston theorem - where can I find a proof?
Nov
18
comment amenable + without $BS(m,n)$+finite $K(G,1)$implies virtually cyclic?
Note for a finite dim. $K(G,1)$, virtually cyclic is equivalent to infinite cyclic (or trivial I suppose), since there can be no torsion.
Nov
5
comment Which mapping class group representations come from algebraic geometry?
It would be interesting if you could flesh out the details of this approach.
Nov
3
comment Classification of elements in mapping class groups
see also flipper by Mark Bell: front.math.ucdavis.edu/1410.1358 bitbucket.org/Mark_Bell/flipper
Nov
2
awarded  Necromancer
Oct
31
awarded  Yearling
Oct
27
comment Can infinitely many alternating knots have the same Alexander polynomial?
No Ryan, Kinoshita-Terasaka is not alternating.
Oct
21
comment Why is it so hard to compute $\pi_n(S^n)$?
I'm at a loss as to what sort of answer you're looking for, but it is funny to contemplate what $\pi_n(S^n)$ would look like if it weren't $\mathbb{Z}$. There is a ring structure coming from composition of maps, which would make $\pi_n(X)$ into a module over this ring for any $X$. But if this ring is not $\mathbb{Z}$, it's hard to envision how one may use this to arrive at a contradiction.
Oct
16
answered Gauss Codes that produce classical knots as opposed to virtual knots
Oct
15
comment discrete group cohomology vs continuous group cohomology for profinite groups
Ok, I guess I had in mind the profinite completion of a finitely generated group, but clearly $G^\delta$ will be infinitely generated if infinite. There are now many finitely generated "good" groups $G$ known, but I don't know whether this implies $\hat{G}^\delta$ is good?
Oct
14
comment discrete group cohomology vs continuous group cohomology for profinite groups
Not sure I understand why this is equivalent to goodness: I thought that was an isomorphism between the cohomology of a group with finite module coefficients and its profinite completion.
Oct
12
comment discrete group cohomology vs continuous group cohomology for profinite groups
This should be true for $H^1$ and $G$ finitely generated by a result of Nikolov and Segal that finite-index subgroups are open.
Oct
11
comment Milnor-Wolf result on growth of solvable groups
Certain special classes of solvable groups are covered by the simple argument in the appendix to Gromov's paper on groups of polynomial growth by Tits. For example, the argument applies to a lattice in a 3-dimensional solvable Lie group. The point is that a finitely generated abelian-by-cyclic group has exponential growth if the cyclic group acts on the abelian subgroup with an eigenvalue $>1$ in absolute value. Maybe one can show that a non-vn solvable group contains such a subgroup or else contains a solvable Baumslag-Solitar subgroup?