Lecture 22 - Mayer-Vietoris Applications

00:00 - The connecting homomorphism
11:35 - Homology groups of the torus
27:45 - Homology of the Klein Bottle
45:33 - Homology of Knot complements

[melissadaniele]

You probably saved me from failing this exam. I'm extremely grateful of the detailed explanation you gave into calculating the induced maps. This was wonderful, thank you very much.!

[n.e.]

I'm so glad you actually went over how to interpret the inclusion and boundary maps. I feel like I understand how to use Mayer-Vietoris, but I have been struggling for days to understand how the various boundary and inclusion maps work, and I could not find a single source discussing these issues. All the sources from Hatcher, to Stack Exchange, to YouTube videos just present the abstract definition, and then show the MV sequences associated with Tori, Klein Bottles, etc., but nobody is willing to explain or address the issue of interpreting the inclusion maps, which is actually the part I find difficult, not the definition of exact sequences or Mayer Vietoris Sequences.

[KaliFissure]

Surface(cos(u/2)cos(v/2), cos(u/2)sin (v/2), sin(u)/2) 0>u>4π 0>v>2π
"Shirley's Surface"
Klein bottle or not ?