bio  website  math.berkeley.edu/~ianagol 

location  Berkeley  
age  44  
visits  member for  5 years, 6 months 
seen  2 hours ago  
stats  profile views  12,283 
I'm a professor at UC Berkeley working predominantly in the field of lowdimensional topology.
4h

comment 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
Nice description. One thing I still don't quite get is why $\Gamma_0$ is generated by the 4 given elements? I don't see how you can deduce this without a bit more information (a free group on 4 elements has many 4 generator subgroups). 
15h

comment 
Can every $\mathbb{Z}^2$ disk be pinballreached?
It seems that you're searching for something like "Sinai billiards". 
16h

comment 
Avoiding meancurvature flow dumbbell neckpinch by inflating a surface
@JosephO'Rourke: Did you mean to discuss Ricci flow? I was confused by the title of your question, since you actually seem to be looking for something related to mean curvature flow. 
1d

comment 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
@QiaochuYuan: Ok, I was using the term "BassSerre tree" incorrectly. I really meant the tree associated to $SL_2$ of a local field, which is a special case of a BruhatTits building. Serre's book Chapter II section 1 is the usual reference. Shalen's notes (linked in my other comment) Chapter 3 also has a nice discussion. 
1d

revised 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
fixed terminology 
2d

revised 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
fixed a mistake computing the quaternion algebra 
2d

comment 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
You're right, I misapplied the theorem since the group is elementary. I'll fix the answer later 
May 2 
comment 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
@QiaochuYuan: Some references are found on Wikipedia: en.wikipedia.org/wiki/Bass%E2%80%93Serre_theory Shalen also covers some of the theory here: dl.dropboxusercontent.com/u/8592391/3manifold%20seminar/… 
May 1 
awarded  Nice Answer 
May 1 
revised 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
added 489 characters in body 
May 1 
answered  Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group? 
May 1 
comment 
Do unit quaternions at vertices of a regular 4simplex, one being 1, generate a free group?
Thinking of these quaternions as elements in $SU(2)$, they have trace $\frac12$. This indicates that there ought to be a nontrivial action on a BassSerre tree. It might be possible to show that the action on this tree is free, in which case the group is free. 
Apr 30 
awarded  mg.metricgeometry 
Apr 27 
comment 
Negatively curved metrics minimizing the length of a homotopy class of simple closed curves
@SelimG: Yes, you're essentially correct. In fact, for a fixed $M$, there are boundedly many curves of bounded length. So a subsequence will preserve the homotopy class of $\gamma$. I should fix the answer to reflect this. 
Apr 25 
comment 
Does this count as a canonical decomposition for nonelementary hyperbolic 3orbifolds?
It is canonical, if you're after a classification of discrete subgroups of $PSL_2(\mathbb{C})$. But Kleinian group theorists usually study such groups up to conjugacy, in which case this does not make a canonical choice for a conjugacy class. One may single out finitely many orbits of points (if it's cofinite volume) by taking points of maximal injectivity radius, for example. 
Apr 24 
comment 
Reduction of selfintersections without reducing the geometric intersection
Yes, the embedded case is just an illustration. 
Apr 24 
revised 
Reduction of selfintersections without reducing the geometric intersection
added 508 characters in body 
Apr 24 
comment 
Reduction of selfintersections without reducing the geometric intersection
@Cusp : I think it's a bit easier to think about the graph when $b$ is embedded. I've added an explanation in this case to clarify, and one may forget about lifting closed arcs unless it helps. 
Apr 23 
answered  Reduction of selfintersections without reducing the geometric intersection 
Apr 23 
revised 
Negatively curved metrics minimizing the length of a homotopy class of simple closed curves
Added more exposition. 