# Orientable Surface

## orientable surface

[‚ȯr·ē‚en·tə·bəl ′sər·fəs]
(mathematics)
A surface for which an object resting on one side of it cannot be moved continuously over it to get to the other side without going around an edge.

## Orientable Surface

a surface that can be oriented. An orientable surface is the opposite of a nonorientable surface. On a nonorientable surface, for example, a Möbius band, there always exist closed curves such that the orientation of a small neighborhood of a point moving along the curve is reversed when the entire curve is traversed. The projective plane is an important example of a closed nonorientable surface.

Mentioned in ?
References in periodicals archive ?
In particular, we obtained a homeomorphism [M.sub.5]([pi]/2) [congruent to] [[summation].sub.5], where [[summation].sub.5] denotes a connected closed orientable surface of genus 5.
For i = 0,1, 2, ..., let [g.sub.i](G) be the number of topologically distinct cellular embeddings of the graph G in the orientable surface [S.sub.i] of genus i.
A map is a connected graph embedded in a compact connected orientable surface in such a way that the regions delimited by the graph, called faces, are homeomorphic to open discs.
Let M be a 3-manifold which is constructed as a fiber bundle over a closed orientable surface with fiber a circle.
Throughout this paper, S will be an orientable surface from [R.sup.3.sub.1] and n its unit normal vector field.
Certainly, on an orientable surface, an equivalence preserve the orientation on this surface.
The proof in the general case is essentially the same, we glue [[summation].sub.1], ..., [[summation].sub.k] cylinders to the surface [M.sub.1] to obtain an orientable surface that is homeomorphic to M.
Henceforth, by surface we shall always mean an orientable surface, equivalently, one which is embeddable in [R.sup.3].
A map M is an embedding of a connected graph G, with possibly multi-edges or loops, into a closed, connected and orientable surface S such that all faces, i.e.
This graph is embedded in a locally orientable surface such that if we cut the graph from the surface, the remaining part consists of connected components called faces or cells, each homeomorphic to an open disk.
A unicellular map is a graph embedded on a compact orientable surface, in such a way that its complement is a topological polygon.
Bender and Canfield ([BC86]) obtained the asymptotic number of maps on a given orientable surface. Gao ([Gao93]) obtained formulas for the asymptotic number of 21-angulations on orientable surfaces, and conjectured a formula for more general families (namely maps where the degrees of the faces are restricted to lie in a given finite subset of 2N).

Site: Follow: Share:
Open / Close