Achim Krause and Thomas Nikolaus: Topological Cyclic Homology

9th November, 2020

This is a 20-lecture course, with each lecture being about 60-90 minutes or so, given in person by Achim Krause and Thomas Nikolaus. It gives an introduction to topological cyclic homology.

  1. Achim Krause and Thomas Nikolaus: Introduction
  2. Thomas Nikolaus: Motivation
  3. Achim Krause: Classical Hochschild Homology
  4. Thomas Nikolaus: The Connes Operator on HH
  5. Thomas Nikolaus: Periodic and Cyclic Homology
  6. Achim Krause: HKR and the Cotangent Complex
  7. Achim Krause: Digression: The Cotangent Complex and Obstruction Theory
  8. Thomas Nikolaus: Digression: Hochschild Homology of Schemes
  9. Achim Krause: Hochschild Homology in ∞-Categories
  10. Achim Krause: Bökstedt Periodicity
  11. Thomas Nikolaus: Properties of THH
  12. Achim Krause: The Circle Action on THH
  13. Thomas Nikolaus: Digression: THH of the Integers
  14. Achim Krause: Negative Topological Cyclic Homology
  15. Achim Krause: Topological Periodic Homology
  16. Thomas Nikolaus: The Cyclotomic Structure
  17. Thomas Nikolaus: The Definition of TC
  18. Thomas Nikolaus: TC of 𝔽p
  19. Thomas Nikolaus: TC of Perfect Rings
  20. Achim Krause: Frobenius Lifts and Group Rings

These videos were produced by the University of Münster, in particular the homotopy theory group there.