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Dec
19
awarded  Necromancer
Nov
5
comment Fantastic properties of Z/2Z
So I guess that the correct reference should be Gromov's "Asymptotic invariants of infinite groups" but it is ~300 pages and I haven't read it. Danny gave a talk at Cornell and in the first ~15 mins he covers the density model and gives a sketch of this result. It's available here: cornell.edu/video/danny-calegari-random-groups-diamonds-glass
Nov
4
answered Fantastic properties of Z/2Z
Oct
13
awarded  Notable Question
Sep
24
revised Is there a table of (fibred knot) monodromies?
Added link to more data.
Jul
2
awarded  Curious
May
9
comment Does small Perron-Frobenius eigenvalue imply small entries for integral matrices?
Thanks, Do you know of any reference for this result?
May
9
accepted Does small Perron-Frobenius eigenvalue imply small entries for integral matrices?
May
9
asked Does small Perron-Frobenius eigenvalue imply small entries for integral matrices?
May
9
awarded  Informed
Apr
1
awarded  Necromancer
Feb
27
comment Is there a table of (fibred knot) monodromies?
For anyone looking for more data like this, significantly more data can now be found at: bitbucket.org/Mark_Bell/bundle-censuses/overview
Feb
27
comment from Dehn twists to surgery diagram
Neil, because of the orientation of $b$, the left Dehn twist $d_\beta$ sends $a$ to $ab^{-1}$ not $ab$. Therefore its matrix in $SL(2, \mathbb{Z})$ is $(1, 0, -1, 1)$. Hence $w$ corresponds to $(0, 1, -1, 1)^6 = (1, 0, 0, 1)$. So $M$ should have Euclidean geometry. By using Alexander's trick on $a \cup b$ you can even check that $(d_\alpha d_\beta)^6 = id$ by hand. Or if you prefer, software packages such as Twister can build the bundle for you and you can check that it is $T^3$.
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awarded  Yearling
Nov
7
awarded  Popular Question
Oct
3
awarded  Caucus
Aug
31
revised Is the normalised Kauffman bracket more powerful than the Kauffman bracket?
title clearer
Aug
31
asked Is the normalised Kauffman bracket more powerful than the Kauffman bracket?
Apr
25
awarded  Nice Question
Feb
28
comment Knot database including text names
Thanks for the suggestion. Just to let you know you can actually skip the volume filtering, Dr. Weeks built it directly into the snappea kernel! Line 90 of isometry.c defines "CRUDE_VOLUME_EPSILON" to be 0.01. Later, around line 140, when testing if two manifolds are isometric if they differ by more than this amount the entire calculation is aborted and the function returns "not isometric".