The angle defect for odd-dimensional simplicial manifolds

Details The angle defect for odd-dimensional simplicial manifolds The angle defect for odd-dimensional simplicial manifolds

2003-10-30

arxiv.org/abs/math/0310473v1

Mathematics

Geometric Topology

19 pages, 2 figures, Latex

Scientific paper

In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect. The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies a Gauss-Bonnet type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least 3), such that the Euler characteristic of the link of each i-simplex equals 2, where i is a non-negative even integer that is less than n. As a corollary, an elementary proof is given that any such simplicial complex has Euler characteristic zero.

Affiliated with

Also associated with

No associations

Rating

The angle defect for odd-dimensional simplicial 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 The angle defect for odd-dimensional simplicial manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The angle defect for odd-dimensional simplicial manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-250888