Quadrilateral-octagon coordinates for almost normal surfaces

Details Quadrilateral-octagon coordinates for almost normal surfaces Quadrilateral-octagon coordinates for almost normal surfaces

2009-04-20

arxiv.org/abs/0904.3041v3

Experimental Mathematics 19 (2010), no. 3, 285-315

Mathematics

Geometric Topology

34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using cohomology, plus other minor changes; v3: Minor housekeepi

Scientific paper

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlying triangulation). Here we develop an analogous theory for octagonal almost normal surfaces, using quadrilateral and octagon coordinates to reduce this dimension from 10n to 6n. As an application, we show that quadrilateral-octagon coordinates can be used exclusively in the streamlined 3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing experimental running times by factors of thousands. We also introduce joint coordinates, a system with only 3n dimensions for octagonal almost normal surfaces that has appealing geometric properties.

Affiliated with

Also associated with

No associations

Rating

Quadrilateral-octagon coordinates for almost normal surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quadrilateral-octagon coordinates for almost normal surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quadrilateral-octagon coordinates for almost normal surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-174188