0. Okay, last post was fun, now let's get into SPECTRAL SEQUENCES, a device to compute #homology groups!
https://en.wikipedia.org/wiki/Spectral_sequence
I hope to unfold a little #tootorial' over the easter holidays, in realtime, pasting as I understand things better.
The uplink is a bit shaky here, and the usual disclaimers apply: about me being easily distracted or getting confused. After all, it's what I do until I finally get it!
#geometry -> #topology -> #homology (#spectralSequence)
2. HOMOLOGY: If you haven't, read this wonderful introduction from our friends at wikipedia:
https://en.wikipedia.org/wiki/Homology_%28mathematics%29
Modern homology is a highly generalized subject. And we'll need some of that generality for spectral sequences to make sense. But to get started it's instructive to stick to classical #homology, on #manifolds.
For these, it's enough to give Betti numbers and torsion, if any. In general context you'd look at chain complexes and work with groups.
Refurio Anachro