Stable Homotopy Seminar, 16: The Whitehead, Hurewicz, Universal Coefficient, and Künneth Theorems
Channel: Paul VanKoughnett
Date: 06/06/2021

These are some generalizations of facts from unstable algebraic topology that are useful for calculating in the category of spectra. The Whitehead and Hurewicz theorems say that a map of connective spectra that's a homology isomorphism is a weak equivalence, and that the lowest nonzero homology group of a connective spectrum is also its lowest nonzero homotopy group. The universal coefficient and Künneth theorems are replaced by spectral sequences computing "generalized homology with coefficients" and homology of smash products; they exist under an "enough projectives"-type condition on the base homology theory discovered by Adams. These topics are also an excuse to define ring and module spectra.

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This is part of the stable homotopy learning seminar organized by Paul VanKoughnett. For notes and more, visit https://www.math.purdue.edu/~pvankoug...