Mastodawn

Refurio Anachro Apr 15, 2017

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)

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Refurio Anachro

3. I'd like to look at de Serre's spectral sequence. It's about manifolds that have been decomposed into fibrations and
I hope it will nurture us with geometric intuition as we go.

A #fibration decomposes a space X into fibers F which intersect the base space B once:

F -> X -> B

Serre spectral sequence: the singular (co)homology of the total space X of a (Serre) fibration in terms of the (co)homology of the base space B and the fiber F.

https://en.wikipedia.org/wiki/Serre_spectral_sequence