Timeline for Once punctured torus bundles in snappy/twister
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 6, 2013 at 23:02 | vote | accept | Neil Hoffman | ||
| Mar 6, 2013 at 23:01 | vote | accept | Neil Hoffman | ||
| Mar 6, 2013 at 23:01 | |||||
| Mar 6, 2013 at 23:01 | vote | accept | Neil Hoffman | ||
| Mar 6, 2013 at 23:01 | |||||
| Mar 6, 2013 at 23:01 | vote | accept | Neil Hoffman | ||
| Mar 6, 2013 at 23:01 | |||||
| Mar 6, 2013 at 23:01 | vote | accept | Neil Hoffman | ||
| Mar 6, 2013 at 23:01 | |||||
| Mar 6, 2013 at 21:51 | comment | added | Sam Nead | I believe the twister page is not relevant -- the b++ etc is "classic" SnapPea notation. | |
| Mar 6, 2013 at 21:46 | answer | added | Sam Nead | timeline score: 3 | |
| Mar 6, 2013 at 20:23 | history | edited | Neil Hoffman | CC BY-SA 3.0 |
I added the link to the snappy function I am trying to call.; deleted 1 characters in body
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| Mar 6, 2013 at 18:34 | comment | added | Ryan Budney | I think Schleimer has documentation for Twister on his webpage. Right, here it is. homepages.warwick.ac.uk/~masgar/Maths/twister.html | |
| Mar 6, 2013 at 17:19 | comment | added | Ian Agol | Every Anosov element of $SL_2(\mathbb{Z})$ is conjugate to a product of $L$ and $R$'s and $\pm I$ (depending on the sign of the trace). This is what SnapPea allows one to do. Elements of $GL_2(\mathbb{Z})$ with negative determinant may be obtained from $SL_2(\mathbb{Z})$ elements by multiplying by a diagonal matrix with $\pm 1$ on the diagonal. So I suspect the notation is indicating a product of $L$'s and $R$'s like you say, together with an adjustment for the sign of the trace and determinant. But it's hard to guess from the notation which corresponds to which. | |
| Mar 6, 2013 at 16:47 | comment | added | Ryan Budney | I haven't seen how Twister has been implemented in SnapPy but I suspect that prefix "b++" or "b+-" probably indicates whether or not you're dealing with an orientable bundle or not -- whether or not the resulting manifold is orientable. The punctured torus has an automorphism group that's technically a little bigger than $SL_2(\mathbb Z)$ since you don't have to be the identity in a neighbourhood of the puncture. The automorphism group is an extension of $SL_2(\mathbb Z)$. The "b+-" prefix probably indicates composition by an orientation-refersing involution. | |
| Mar 6, 2013 at 16:13 | history | asked | Neil Hoffman | CC BY-SA 3.0 |