The angle defect for odd-dimensional simplicial manifolds
| dc.creator | Bloch, Ethan D. | |
| dc.date | 2003-10-30 | |
| dc.date.accessioned | 2026-07-07T05:02:21Z | |
| dc.date.available | 2026-07-07T05:02:21Z | |
| dc.description | 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. | |
| dc.description | 19 pages, 2 figures, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0310473 | |
| dc.identifier | http://arxiv.org/abs/math/0310473 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69026 | |
| dc.subject | Geometric Topology | |
| dc.subject | Combinatorics | |
| dc.subject | 52B70 (Primary) | |
| dc.title | The angle defect for odd-dimensional simplicial manifolds | |
| dc.type | text |