Stable Homotopy Seminar, 12: The Atiyah-Hirzebruch Spectral Sequence (Caleb Ji)
Channel: Paul VanKoughnett
Date: 2021-05-10

Caleb Ji gives us an overview of spectral sequences, focusing on the example of the Leray-Serre spectral sequence which is used to prove the equivalence of cellular and singular homology. He then defines the Atiyah-Hirzebruch spectral sequence, which is used to compute extraordinary cohomology of a space or spectrum in terms of its ordinary cohomology. This is maybe our first example that these extraordinary cohomology theories can be actually computable. Caleb ends with several example computations related to K-theory of projective spaces.

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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/spectra/index.html