Minimal Triangulations of Manifolds

Details Minimal Triangulations of Manifolds Minimal Triangulations of Manifolds

2007-01-25

arxiv.org/abs/math/0701735v1

Mathematics

Geometric Topology

Survey article, 29 pages

Scientific paper

In this survey article, we are interested on minimal triangulations of closed pl manifolds. We present a brief survey on the works done in last 25 years on the following: (i) Finding the minimal number of vertices required to triangulate a given pl manifold. (ii) Given positive integers $n$ and $d$, construction of $n$-vertex triangulations of different $d$-dimensional pl manifolds. (iii) Classifications of all the triangulations of a given pl manifold with same number of vertices. In Section 1, we have given all the definitions which are required for the remaining part of this article. In Section 2, we have presented a very brief history of triangulations of manifolds. In Section 3, we have presented examples of several vertex-minimal triangulations. In Section 4, we have presented some interesting results on triangulations of manifolds. In particular, we have stated the Lower Bound Theorem and the Upper Bound Theorem. In Section 5, we have stated several results on minimal triangulations without proofs. Proofs are available in the references mentioned there.

Affiliated with

Also associated with

No associations

Rating

Minimal Triangulations of Manifolds 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 Minimal Triangulations of Manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal Triangulations of Manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-329157