O.K, please let me see if I got it right:(adsbygoogle = window.adsbygoogle || []).push({});

Let M be an orientable m-manifold with non-empty boundary B.

Let p be a point in B , and let {del/delX^1,...,del/delX^(m-1) }_p

be a basis for T_pB for every p in a boundary component .

Let N be a unit normal field on B . Now, this is the induced orientation (is it?):

We consider the collection {N_p, del/delX^1,...,delX^(m-1)}_p

(with N_p normal to M at p.)

AS IF p were a point in M, and not in the boundary B, (e.g., we can

smooth out the boundary so that it disappears, or we can cap

a disk or something, so that one boundary component disappears).

Then, if this basis {N_p, del/delX^1,...,delX^(m-1)}_p for p in M

of T_pM is oriented in agreement with the given orientation of M, (Jacobian of

chart overlap is positive, etc. ) then the boundary is positively oriented,

otherwise it is negatively oriented.

Is this it?

Thanks.

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# Induced Orientation on Mfld. Boundary.

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