Notes on Orb
Orb is a software package developed by Damian Heard (as part of a
PhD supervised by Craig Hodgson), which uses Jeff Weeks'
SnapPea kernel to study orbifolds.
Currently, orb is available from Craig Hodgson's website: here. We provide a
chunky version here:
This version is easy to download and run on macs running OS 10.6.8.
Linux users can download
orb from Craig's website. Windows users might need to get a virtual box
running and use the linux version. (Sorry that's not a better answer.)
Note: Orb relies on qt version 3 or so and eventually the graphical interface
will be obsolete.
We now describe how to input an orbifold into Orb and take its two fold cover.
First open orb and click on the notepad button . This should open the following window:
We now draw in the orbifold singular set as if it were a stick knot. The only difference is that Orb
treats the two vertices of order 4 as cusps.
Next, we send this tangle to be investigated by clicking on the button.
This will bring up a need window. We can label each strand of the singular set by order 2 points in the following way.
Enter 2's in the top left:
Then click update. Next we build a cover by selecting aka the magic wand.
The following menu pops up:
First we select build cover, enter 2 for the covering degree and select the cover with $Z+Z+Z/5Z$ homology.
Next, we select the magic wand again and choose the prune graph from the menu that pops up.
Finally, we select export to snappea from this menu.
If you import this triangulation into snappy, you can see it is the triangulation of 't12060'.