June 4, Gerben: Multiplicative structure in the Adams spectral sequence. May 28, Stan: The E_2-page of the Adams spectral sequence and the first few stable stems. May 21, Antonie: Setting up the Adams spectral sequence. This means that if we view our groups as being located at points of the integer lattice on the. May 7, Lennart: Introduction to stable homotopy theory, II. The spectral sequence that we consider is first-quadrant. Sven's notes and exercises.Īpr 30, Lennart: Introduction to stable homotopy theory, I. Max' exercises.Īpr 23, Sven: Cohomology of Eilenberg-MacLane spaces.
#Spectral sequences mod
Stan's notes and exercises.Īpr 16, Max: The mod C Whitehead theorem, rational homotopy groups of spheres, the first p-torsion in the homotopy groups of spheres. The mod C Hurewicz theorem, homotopy groups of spheres are finitely generated. Wessel's notes and exercises.Īpr 9, Stan: Serre class theory. Tor and Ext, the Künneth and Universal Coefficient spectral sequences. Mar 26, Wessel: Spectral sequences in homological algebra. The Hurewicz theorem, some homotopy groups of spheres. Mar 19, Martijn: First applications of the Serre spectral sequence. Mar 12, Max: More on the Serre spectral sequence. The Dress construction of the Serre spectral sequence. Mar 5, Antonie: The spectral sequences of a filtered complex and of a double complex. Sven's notes and exercises.įeb 26, Gerben: Spectral sequences, definitions and first examples. Fibrations, Eilenberg-MacLane spaces, Postnikov towers, loop spaces. I do not believe their proof uses anything about the Serre spectral sequence beyond the fact it is a spectral sequence of differential graded algebras whose E 2 page is of the form H ( B K) H ( F K) (when K is a field), so it should give a purely algebraic result about spectral sequences with E 2 pages of this form.
Starting April 30, the seminar will move to the timeslot 1-3pm, still on Fridays.įeb 19, Sven: Review of basic homotopy theory. The seminar will take place on Fridays, 3-5pm, through Zoom. Along the way we will discuss some of the basics of stable homotopy theory.
The main examples we will consider are the Serre spectral sequence and the Adams spectral sequence. The goal is to get acquainted with spectral sequences as a computational tool in algebraic topology. In Spring 2021, Lennart Meier and I will be running a seminar for MSc students on spectral sequences.
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