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Homotopy theory, homological algebra, algebraic treatments of manifolds.

29 votes
4 answers
2k views

Geometric interpretation of the lower central series for the fundamental group?

For any group $G$ we can form the lower central series of normal subgroups by taking $G_0 = G$, $G_1 = [G,G]$, $G_{i+1} = [G,G_i]$. We can check this gives a normal chain $$G_0 \ge G_1 \ge ... \ge G_i …
28 votes
5 answers
4k views

Modern source for spectra (including ring spectra)

I am looking for a modern introduction to spectra that improves on the treatment by Adams in his "Stable Homotopy and Generalized Homology" notes (by improves I mean taking into account what has been …