Stable Homotopy Seminar, 20: Computations with the Adams Spectral Sequence (Jacob Hegna)
Channel: Paul VanKoughnett
Date: 05/07/2021

Jacob Hegna walks us through some of the methods which have been used to compute the E_2 page of the Adams spectral sequence for the sphere, a.k.a. Ext_A(F_2, F_2), where A is the Steenrod algebra. The May spectral sequence works by filtering A and first computing Ext over the associated graded. The Lambda algebra is a small algebra equivalent to the cobar complex, arising from Koszul duality. More recently, Isaksen and collaborators have been making huge progress using related Adams spectral sequences coming from motivic stable homotopy theory.


Jacob then turns to spectra such as ko, tmf, and MO, which have simple presentations for their mod 2 cohomology and thus simple Adams spectral sequences. He computes the homotopy groups of ko (i.e. real Bott periodicity) and of MO (i.e. the unoriented cobordism groups).

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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.