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Mar
23
awarded  Enlightened
Mar
23
awarded  Nice Answer
Mar
13
answered 2-bridge knots in the Rolfsen's table
Mar
9
awarded  Nice Answer
Jan
10
awarded  Yearling
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
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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
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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 $T^3$.
Jan
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awarded  Yearling
Nov
7
awarded  Popular Question