Dear Colleagues and Friends,


Here's a question that I hope some of you, more experienced in programming, can answer.


Once SnapPy is used to compute the symmetry group of a hyperbolic manifold by way of, say,



> 
> K = Manifold('4\_1');
> 
> 
> S = K.symmetry\_group();
> 
> 
> 


it outputs the action of the isometries on the cusps as



> 
> S.isometries()
> 
> 
> 



```
[0 -> 0
[1 0] 
[0 1] 
Extends to link, 
0 -> 0
[-1 0]
[ 0 1]
Extends to link, 
0 -> 0
[1 0] 
[0 1] 
Extends to link, ... etc

```

As you may imagine, the 0th entry is the identity map (a good one to start the list with), but the 2nd one is not, although its action on the cusp is trivial (SnapPy also says it's an involution, since S.multiply\_elements(2,2) returns 0).


Is there a way to see the symmetry group action on the rest of the manifold in this case (as a callable method within SnapPy)?


Cheers,
Sasha



SnapPy isometry routine
As Ryan says, "isomorphisms of triangulations" are computed under the hood in snappy (and that is how it computes symmetry groups). However, this functionality is not shown to the user. 


If you have a convincing use case, you could contact Nathan Dunfield and Marc Culler with your request.


