[SnapPea-planning] priorities

[Bill Thurston]

Nathaniel et All,
	That's a nice list---any signficant progress on this would be great!
	Another long-term item, but probably not for this list, which is  
already very ambitious: more systematic treatment of various kinds of  
incompressible surfaces. This goes hand-in-hand with dealing with non- 
hyperbolic manifolds (as snappea already reports in the case of  
suspected spheres, disks, annuli, etc.) but there are other cases that  
are natural.
	In addition (long-term project): a way to systematically handle  
manifolds with higher-genus boundary, and to compute hyperbolic  
structures of infinite volume, perhaps by capping them off in standard  
ways (e.g., gluing on handlebodies as higher-genus fillings,  choosing  
a maximal family of curves to make parabolic, or even finding a way to  
apply the uniformization theory).
	I don't know anything about Sage, but I suppose a major goal should  
be to have a robust and simple system for extensions and plugins as  
well as for export and import of descriptions of manifolds and  
geometry. It would be especially wonderful if it didn't require  
substantial technical experience in programming to contribute a useful  
extension.
	Bill
On Apr 27, 2009, at 5:21 AM, Nathaniel Thurston wrote:

> Dear All,
>
> I've been in contact with Michael Douglas at the Simons Institute (is
> that the right name?), and he's suggested that the institute would
> have funding for at least a month's work and asked me to determine the
> relative priority of the work to be done.  I examined the mailing list
> history, and came up with the this outline:
>
> 1. finish tcl port (cross-platform graphics; test for mac osx & linux
> compatibility)
> 2. sage interface
> 3. more robust Dirchlet domain algorithm
> 4. requests (grouped by estimated effort required, and ordered by time
> of request)
> 	a. short-term
> 		identify dehn-drilling axes in viewer [Bill Thurston]
> 	b. medium-term
> 		good drillings view [Bill Thurston]
> 		integrated hyberbolic viewer [Bill Thurston]
> 		symbolic math for smith normal form [Marc Culler]
> 		direct computation of Chern-Simons invariant [Marc Culler]
> 		more robust generator of short geodesics [Dylan Thurston]
> 	c. long-term
> 		looking for supergroups of finite index [Bill Thurston]
> 		detriangulate command: manifold -> link complement [Bill Thurston]
> 		dealing with non-hyperbolic manifolds [Dylan Thurston]
> 		rewrite snap in sage [Nathan Dunfield]
>
> Would anyone like to amend this list before I send it out to the
> SnapPea-summary mailing list?
>
> Best Regards,
> 	Nathaniel
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