in the Stable Stem

Beginning of the E2 page of the Adams SS. Source: Schwede's symmetric spectra

In Fall 2018, the homotopy theory learning seminar is on families of elements in the stable ho­motopy groups of the spheres, following Ravenel's green book [Rav86]. This seminar is organized by Arun Debray and Richard Wong.


Planning meeting and overview
Richard, September 5

Introduction to spectra
Rok, September 10

Spectral sequences: construction and use
Ricky and Arun, September 17

The Adams and Adams-Novikov spectral sequences
Riccardo, Alberto, and Richard, September 24, October 1, and October 8
[Rav86] §§2.2, 4.4

Construction of BP and MU
Ty, October 22

Hopf algebroids
Rok, October 29

Some calculations with BP*BP
Riccardo, November 5
[Rav86] §4.3

First calculations with the Adams-Novikov spectral sequence
Arun, November 12
[Rav86] §4.4

Greek letter elements, etc.
Richard, November 19
[Rav86] §5.1

Hopf invariant one
Arun, Riccardo, and Alberto, November 26 and December 3
[Rav86] §5.2

The image of J
Rok, Ty, and Ricky (possibly), December 10
[Rav86] §5.3

Main references:

Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres.

Related links:

Agnès Beaudry and Jonathan Campbell, “A Guide for Computing Stable Homotopy Groups.”
John Rognes, “The Adams spectral sequence.”