Stable Homotopy Seminar, 17: Universal Coefficient Theorem, Moore Spectra, and Limits

We finish constructing the universal coefficient spectral sequence, and look at some classical examples involving Moore spectra. As it turns out, it's really easy in stable homotopy theory to invert or localize at a prime. In particular, *rational* stable homotopy theory is completely algebraic, being equivalent to the theory of chain complexes over Q. Next, we look at inverse limits of towers and construct the "Milnor exact sequence" computing their homotopy groups -- this recovers a familiar calculation of the cohomology of an infinite CW-complex. Finally, we briefly look at Postnikov towers (which are also very simple to construct in the stable world.)

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