Subdivisions, shellability, and the Zeeman conjecture

Details Subdivisions, shellability, and the Zeeman conjecture Subdivisions, shellability, and the Zeeman conjecture

2012-02-29

arxiv.org/abs/1202.6606v2

Mathematics

Combinatorics

18 pages, 5 figures. Added subsection 3.2 on collapsibility of products with intervals. Section 4 largely rewritten, improved

Scientific paper

We prove the (d-2)-nd barycentric subdivision of every convex d-complex is shellable. This yields a new characterization of the PL property in terms of shellability: A triangulation of a sphere or of a ball is PL if and only if it becomes shellable after sufficiently many barycentric subdivisions. This improves results by Whitehead, Zeeman and Glaser. We also show that any contractible complex can be made collapsible by repeatedly taking products with an interval. This strengthens results by Dierker and Lickorish. Finally, we show that the Zeeman conjecture is equivalent to the statement "the product of any contractible 2-complex with an interval becomes (simplicially) collapsible after a suitable number of barycentric subdivisions". This number cannot be bounded: For any two positive integers m, n, we construct a 2-complex C such that sd^m (C x I^n) is not collapsible.

Affiliated with

Also associated with

No associations

Rating

Subdivisions, shellability, and the Zeeman conjecture 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 Subdivisions, shellability, and the Zeeman conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Subdivisions, shellability, and the Zeeman conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-525293