I have been trying to learn about snappy's method for encoding once-punctured torus bundles (<http://www.math.uic.edu/t3m/SnapPy/manifold.html#snappy.Manifold>). As you can see from the link, they are imported via the Manifold() function.


I have looked through documentation on the snappy website and much of the twister website. I am having trouble finding a reference for the encoding ‘b++LLR’, ‘b+-llR’, ‘bo-RRL’, ‘bn+LRLR’.


Following the literature (see for example <http://arxiv.org/pdf/math/0406242.pdf>), I am guessing that $L$ and $R$ correspond to writing an element in $SL(2,\mathbb{Z})$ as a word in 


$L = \begin{pmatrix} 1 & 0 \\\\ 1 & 1 \end{pmatrix}$ and $R = \begin{pmatrix} 1 & 1 \\\\ 0 & 1 \end{pmatrix}$ with lower case elements used for inverses. 


However, what to the b++, b+-, bn+ and bo- denote? 



Once punctured torus bundles in snappy/twister
I believe that your question is answered by section (3e) at [this](http://www.geom.uiuc.edu/software/snappea/) page at the Geometry Center. Note that b+ and bo are equivalent as are b- and bn (o and n stand for orientation preserving and reversing, respectively). You can check a few examples using the is\_isometric method of Manifold.


