Reputation
34,973
Next tag badge:
128/100 score
18/20 answers
Badges
1 80 165
Newest
 Necromancer
Impact
~636k people reached

2d
comment When does a CAT(0) group contain a rank one isometry
Ah, good point, I missed that hypothesis. In any case, it seems like your question is as difficult as the flat closing conjecture.
2d
comment When does a CAT(0) group contain a rank one isometry
This seems like it would follow from the rank rigidity conjecture of Ballmann and Buyalo and this result: ams.org/mathscinet-getitem?mr=3095707
Apr
30
comment Looking for examples of large hyperbolic two-generator knots or 3-manifolds
You're welcome @Charlie (Frohman? Livingston? Trotter?).
Apr
29
answered Looking for examples of large hyperbolic two-generator knots or 3-manifolds
Apr
29
comment Looking for examples of large hyperbolic two-generator knots or 3-manifolds
For the answer to your second question, one may find hyperbolic 3-manifolds with Heegaard genus 2 and $b_1 >0$, which are thus large with rank 2 fundamental group. I suspect knot examples exist, but I'll have to think about it.
Apr
23
comment Are braid groups conjugacy separable?
For the 3-strand braid group, which is isomorphic to the fundamental group of the trefoil knot complement, a Seifert-fibered manifold with boundary, conjugacy separability was proved e.g. here: ams.org/mathscinet-getitem?mr=1980432
Apr
22
comment Finitely presented amenable LERF group which is not virtually solvable
As far as I know, Grigorchuk has an example satisfying 1., 2., 3., but not 4. dx.doi.org/10.1070/SM1998v189n01ABEH000293 But this group is not residually finite, much less LERF.
Apr
17
revised Is there a degree one map from a product $B\times S^1 \to \#_n S^2 \times S^1$ for any n
added 725 characters in body
Apr
15
answered Is there a degree one map from a product $B\times S^1 \to \#_n S^2 \times S^1$ for any n
Apr
12
comment Symmetry conjecture for minimal dilatation pseudo Anosov mapping classes
Constructions of this sort are made in this paper, but no conjecture stated: msp.org/gt/2009/13-4/p10.xhtml
Apr
4
comment Is there a complex structure on the 6-sphere?
Here is the erratum: dx.doi.org/10.1063/1.4930560
Apr
4
comment Is there a complex structure on the 6-sphere?
This question was duplicated here: mathoverflow.net/q/210089/1345 A commenter @YangMills queried a claim in the Etesi paper, which led to the publication of an erratum.
Apr
3
comment Braid groups over the sphere
Linearity is overkill, residual finiteness suffices for a finitely generated group to be Hopfian, and this is a much older result.
Mar
25
awarded  Necromancer
Mar
23
comment Compatibility of spherical and hyperbolic geometry for fibred knots
It is believed that hyperbolic 3-manifolds cannot be foliated by minimal surfaces. See: arxiv.org/abs/1512.04145, arxiv.org/abs/1512.03858
Mar
22
comment Fibered knots vs Heegaard genus
@magicker72: okay, correct, I fixed that. In any case, one can make the distance arbitrarily large by taking powers of the gluing map. One remark: most likely there are much simpler examples, namely lens spaces, but I wasn't sure if this is known (Ken might know a reference).
Mar
22
revised Fibered knots vs Heegaard genus
added 1 character in body
Mar
22
answered Fibered knots vs Heegaard genus
Mar
15
comment Do smooth manifolds admit linear atlases?
Such a manifold would be affine, although your condition is a bit stronger. en.wikipedia.org/wiki/Affine_manifold
Mar
13
comment How many non-commensurable non-arithmetic manifolds have a quaternion algebra like this?
yes, that's right. The doubling procedure ("inbreeding") described in the above paper ought to preserve the quaternion algebra, since the reflection involution lies in the commensurator. One may make a sequence of non-congruence manifolds this way with arbitrarily small injectivity radius, and hence in infinitely many commensurability classes (Margulis' theorem implies that a non-arithmetic group has discrete commensurator, hence a lower bound on the systole).