Orientation

Orientations and Homology, Pg233-235 Allen Hatcher (copied from Hatcher).

[HarpreetBedimath]

Hi There, the second slide does start abruptly, I added the first slide later in order to give some sort of an easier to understand case before going to Manifold M.

[eolfeci]

I see. It would have been nice also to see how this homology version of orientation relates to the more common one in terms of a basis. But overall I think your slides are quite good and would be helpful to someone learning the subject. Keep it up!

[eolfeci]

Hi Harpreet. Or is it Bedi?

I feel there is something missing between the first two slides. In slide #1, you show why H^n(R^n|x) is infinite cyclic... and then in slide #2, you start talking about M without saying what it is (a topological n-manifold), and you claim that H^n(M|x) is infinite cyclic. Again, I feel this is a little abrupt. The argument of course is that by excision, we have H^n(M|x)=H^n (U|x), where U is any nbhd of x homeomorphic to R^n. And then of course H^n (U|x)=H^n (R^n|x).