orientable's Usage Examples:

A manifold is orientable if it has a consistent choice of orientation, and a connected orientable manifold has exactly two different.

an (orientable) surface, is the number of "holes" it has, so that a sphere has genus 0 and a torus has genus 1.

The genus of a connected, orientable surface.

branch of mathematics, the Klein bottle (/ˈklaɪn/) is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining.

mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs.

manifold admits a nowhere-vanishing volume form if and only if it is orientable.

An orientable manifold has infinitely many volume forms, since multiplying a.

{\displaystyle o_{1}} if B is orientable and M is orientable.

o 2 {\displaystyle o_{2}} if B is orientable and M is not orientable.

considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold that contains an orientable, incompressible.

the fundamental class is a homology class [M] associated to a connected orientable compact manifold of dimension n, which corresponds to the generator of.

be embedded in an orientable surface of (orientable) genus n / 2 {\displaystyle n/2} or in a non-orientable surface of (non-orientable) genus n {\displaystyle.

In general, a surface is said to be orientable if it does not contain a homeomorphic copy of the Möbius strip; intuitively.

odd-dimensional non-orientable manifolds, via the two-to-one orientable double cover.

The Euler characteristic of a closed orientable surface can be calculated.

{\displaystyle 1-\chi (S),\,} taken over all compact, connected, non-orientable surfaces S bounding K; here χ {\displaystyle \chi } is the Euler characteristic.

arbitrarily re-oriented in this way, the surface as a whole is said to be non-orientable.

Lickorish–Wallace theorem in the theory of 3-manifolds states that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a.

orientable, as well.

The standard Möbius strip has the unknot for a boundary but is not a Seifert surface for the unknot because it is not orientable.

The genus of a connected orientable surface is an integer representing the maximum number of cuttings along.

In differential geometry, given a spin structure on an n-dimensional orientable Riemannian manifold (M, g), a section of the spinor bundle S is called.

prime decomposition theorem for 3-manifolds states that every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) finite.