What vector makes this surface Haken?

[WPettersson]

Request from Neil. It would be nice to see (in the UI) exactly what vector makes a manifold Haken. This is technically calculated in the engine but not available (to any interface), and is only calculated if cheaper tests fail to determine Haken-ness.

[delooper]

I'm a little confused by the request. Is this a request for an incompressible surface, given in some normal coordinate system?

[baburton]

I'm a little confused by the request. Is this a request for an incompressible surface, given in some normal coordinate system?

This was how I interpreted it. - b.

[WPettersson]

Yes, sorry, I meant vector in some normal coordinate system.

[delooper]

I don't recall all the details of the algorithm Regina uses, but my impression was it's "mostly short-cuts" where you don't usually get an explicit incompressible surface, at least, not one that's readily computed with respect to the original triangulation.

Perhaps the easiest way to deal with this request would be to write a supplementary algorithm -- once it's verified to be Haken, enumerate normal surfaces of whatever kind it takes (?vertex normal?) and run through them using the incompressibility test.

Do you know if Neil needs the algorithm to be fast, or is it just a "nice to see" thing, as you say?

[baburton]

I don't recall the algorithm Regina uses precisely, but my impression was it's "mostly short-cuts" where you don't usually get an explicit incompressible surface, at least, not one that's readily computed with respect to the original triangulation.

It’s more the other way around: showing non-Hakenness involves taking every vertex surface and using short-cuts to find compressing discs. Showing Hakenness in regina does typically mean you have your hands on an explicit vertex surface that you have certified to be incompressible. - b.