[SnapPea-planning] priorities

[Bill Thurston]

I could come up with some more contributions to a list of potential  
projects if that's what you want. I'm sure others also have many ideas  
--- for example, I hope many of Nathan's projects will get integrated  
into a common public version.  But what's a good way to proceed?   One  
question:  should the goal be to evolve snappea into a more general  
environment for low-dimensional geometry and topology, or should the  
aim be for it to be a unit that does one cluster of things well, with  
a good interface that can interact well with other independently- 
useful programs?

For example: surfaces,  automorphisms of surface groups, geometric  
decompositions for mapping tori --- this is a somewhat self-contained  
theory. But, a mapping torus is a 3-manifold that can be looked at in  
other ways,  recognition is a natural snappea function. And,  the  
geometry of the mapping class group is intimately related to the  
geometry of quasifuchsian 3-manifolds; how do you find surfaces  
immersed or embedded in a a 3-manifold and then analyze them?   This  
also connects to computing and investigating minimal surfaces and  
harmonic surfaces and pleated surfaces.   Using decompositions of 3- 
manifolds by cutting along subdivisions using minimal disks for the 2- 
skeleton is one idea I've thought might do well at exploring the  
geometry of the Dehn filling space when ideal tetrahedra become  
negatively oriented.  This might extend to analyzing Dehn fillng  
spaces for cone manifolds iwth other geometries; if so, it could  
become a very powerful tool within snappea.

So --- it's not obvious to me the extent to which it's better (in the  
long run) to separate the different aspects of geometry and topology,  
communicating perhaps by  human-legible and editable ascii files vs.  
the extent to which it's better to aim for a single integrated master  
program whose inner workings are more shielded.

	Bill

On Apr 28, 2009, at 11:11 AM, Nathaniel Thurston wrote:

> The list is pretty ambitious, and I like the notion of making it even
> more so.  If we record what we want, it's just possible that we might
> be able to do it...