Algebraic Topology 15: Exact Sequence of Homology and Excision

[@swaruppaul4417]

Please continue this series! I request you to cover cohomology !

[@DDranks]

48:52 Never thought of this, but indeed, really intuitive once you think about it, and the openness seems indeed crucial, as it provides necessary "extent" at each dimension so that the sets really "use up" dimensions n and m.

[@DDranks]

I didn't really see the motivation for exact sequences and diagram chasing, until the end. But now I think I'm starting to see it. The sequences provide algebraic "connections" between related spaces strong enough to get some results that would be hard to get otherwise.

[@sauravkumar-qk7tg]

At 28:10 you have written del(b)=b', commutativity cannot give this we need injectivity of j to obtain this result but still the proof works because the difference lies in the kernel.

[@DDranks]

50:41 Don't you mean "Z" instead of "X" here? X seems to correspond to R^m, so setting Z = R^m-U makes X-Z to equal U.

[@sayanghosh6544]

It's Great, Professor! : )

[@ompatel9017]

Woah interesting I love homological algebra

[@-minushyphen1two379]

00:00 Proof of that theorem about long exact sequences of homology groups of a short exact sequence of chain complexes by diagram chasing 33:05 Motivation of relative homology and good pairs as applications 43:00 Statement (not proof) of the Excision Theorem 46:40 Using the Excision Theorem to prove that open balls of different dimensions must not be homeomorphic

[@depressedguy9467]

finally relative homology

[@depressedguy9467]

I want cohomology