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

1. A spectral sequence is really a 3d grid, a #lattice of rank 3. It's points are labeled with integer coordinates p,q,r and to each point we associate a group E:

E_pq^r

By convention the coordinate p goes to the right, q up, and r picks a sheet. We'll be working with one sheet at a time.

To move around we'll need a 'boundary operator' or 'differential' d_r, which is just a function with a peculiar property:

d_r(d_r(E)) = 0

And 'bidegree' (-r,r-1).

This is chinese for you? Read on...