parallelizable

If the whole problem was parallelizable, we would, of course, expect the speed up to double also.

A manifold that does have a global moving frame is called parallelizable.

A classical problem was to determine which of the spheres S are parallelizable.

The case S is the circle, which is parallelizable as has already been explained.

The hairy ball theorem shows that S is not parallelizable.

"People have thought the problems we have parallelized were not parallelizable."

Further, a given problem may accommodate different algorithms, which may be more or less parallelizable.

In particular, a noncompact world manifold must be parallelizable.

In this case, the manifold is called parallelizable.

A loop is considered parallelizable if doesn't contain any cross-iteration data dependences.

This still requires the developer to know that the loop is parallelizable, but all the other work is done by the library.

Since not every manifold is parallelizable, a tetrad can generally only be chosen locally.

In other words, is parallelizable if and only if is a trivial bundle.

Then is equal to , and is clearly parallelizable.

This implies that the 3-sphere is parallelizable.

For this reason parallel computing is relevant only for a low number of processors and very parallelizable programs.

A smooth manifold is parallelizable if it admits a smooth global frame.

A manifold is called parallelizable whenever admits a parallelization.

Every Lie group is a parallelizable manifold.

Every affine space, considered as manifold, is parallelizable.

Proving that other spheres are not parallelizable is more difficult, and requires algebraic topology.

A global section will exist (by definition) only when M is parallelizable, which implies strong topological restrictions.

Therefore, the sphere is not parallelizable.

Thus tangent planes along a curve can be identified using the intrinsic geometry, even when the surface itself is not parallelizable.

In particular, every Hilbert manifold is parallelizable.