Is the idea of thickness actually required to specify assimilation on nonorientable manifolds?

I am attempting to recognize, in as straightforward terms as feasible:

  1. How to specify assimilation for non - orientable manifolds, and also
  2. why it is difficult to do so making use of just differential kinds.

Specifically, I've seen some conversation of making use of "thickness" as opposed to $n$ - kinds for assimilation, yet am not actually clear on why thickness are called for. To put it simply, is it actually difficult to specify assimilation on nonorientable manifolds making use of kinds alone?

I am certainly mindful that any kind of $n$ - kind have to disappear someplace on a nonorientable manifold, so we can not locate a quantity kind, therefore can not make use of the typical definition of assimilation. I assume the factor I'm not locating this solution pleasing is that it is a little bit tautological: we can not specify assimilation relative to quantity kinds due to the fact that there are no quantity kinds. Yet why must we specify assimilation relative to a (international) quantity kind to begin with? Exists actually nothing else means to do it making use of in your area - specified kinds? Considering a manifold as a collection of neighborhood graphes prevails in geometry, and also I'm having problem recognizing why this strategy does not operate in the instance of assimilation.

2019-05-18 21:44:56
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Answers: 1

On an orientable manifold, we specify assimilation of features relative to a quantity kind . On a non orientable manifold, there are no quantity kinds, so we need to do another thing!

2019-05-21 17:37:42