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

4. A chain complex C(X) is a notation to encode information about a space X. It comes as a list of abelian-, which are very simple, groups

... E_2 -> E_1 -> E_0 -> 0

connected by maps (differentials, boundary operators), one for every arrow:

d_1: E_1 -> E_0

such that applying two consecutive ones to any element yields an identity element:

d_1(d_2(e)) = id_E_0

For example: ... (read on)

#chainComplex #boundaryOperator #differential