On locally constructible spheres and balls

Details On locally constructible spheres and balls On locally constructible spheres and balls

2009-02-03

arxiv.org/abs/0902.0436v4

Acta Mat.206:205-243,2011

Mathematics

Combinatorics

Revised version, with corrections (31 pages, 6 figures)

Scientific paper

10.1007/s11511-011-0062-2

Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) 3-spheres and showed that there are only exponentially-many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC property for d-spheres ("the sphere minus a facet collapses to a (d-2)-complex") and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and obtain hierarchies of such properties for simplicial balls and spheres. The main corollaries from this study are: 1.) Not all simplicial 3-spheres are locally constructible. (This solves a problem by Durhuus and Jonsson.) 2.) There are only exponentially many shellable simplicial 3-spheres with given number of facets. (This answers a question by Kalai.) 3.) All simplicial constructible 3-balls are collapsible. (This answers a question by Hachimori.) 4.) Not every collapsible 3-ball collapses onto its boundary minus a facet. (This property appears in papers by Chillingworth and Lickorish.)

Affiliated with

Also associated with

No associations

Rating

On locally constructible spheres and balls 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 On locally constructible spheres and balls, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On locally constructible spheres and balls will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-296966