Spezielle Kapitel der Topologie 2023

Here is a list of topics for my set of lectures for the special topics course in Wuppertal this (Summer 2023) semester. The list will be updated after each lecture, so that irregular participants can decide whether they would like to join on short notice. I will also upload handwritten notes after each lecture.

Each topic is intended to cover roughly 40 minutes of the 90 minute time-slot, which will include a 10 minute break.

The usual lecture times are Monday (G.13.18) and Wednesday (G.15.25) between 12:15 and 13:45. In addition, there will also be a lecture on the Fridays 23.06 and 30.06, in G.15.25 between 14:15 and 15:45.

Topic Day
Overview and motivation 14.06.23
Module of differentials 14.06.23
The cotangent complex 19.06.23
Properties of the cotangent complex 19.06.23
Review cotangent complex; cotangent complex of a regular quotient 21.06.23
Hochschild homology 21.06.23
Hochschild homology of truncated polynomial rings 23.06.23
Homotopy ring of a simplicial commutative ring 23.06.23
Spectral sequences 26.06.23
Hochschild homology of polynomial rings 26.06.23
The André--Quillen spectral sequence 28.06.23
---=--- 28.06.23
Smooth ring maps and proof of HKR 30.06.23
Further properties of Hochschild homology 30.06.23
The B-operator on Hochschild homology 10.07.23
The Loday construction 10.07.23
Quillen's cotangent complex formalism 12.07.23
---=--- 12.07.23

© 2023 Tommy Lundemo
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