Denis Nardin's Home Page
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Universität Regensburg
93040 Regensburg
Deutschland
Zimmer M223
denis DOT nardin AT ur DOT de
WiSe 2020 - Introduction to stable homotopy theory
Lectures: Mo 10-12, Th 10-12Exercise sessions: We 12-14
This class will cover the construction and the basic properties of the category of spectra, an important mathematical tool with applications to homotopy theory, geometric topology, number theory and algebraic geometry. Planned topics include:
- Construction of the category of spectra
- The recognition principle, following Segal
- Monoidal structures and duality
- Localization and completion
- Thom spectra and manifolds
The course will be held on Zoom. If you are not a student of the University of Regensburg and you're interested in attending, please email me.
You can find the (partial) notes for this class here.
You can find the videos of the lectures here.
Notes for the class: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25.
Exercises
The solutions of the exercises must be sent via email to Pavel Sechin before 23:59 of the due date.
The subject of the email must be "Stable Homotopy Theory - Exercise Sheet N", where "N" is the number of the exercise sheet.
- Exercise sheet 1 Due on Sunday November 15th
- Exercise sheet 2 Due on Sunday November 22nd
- Exercise sheet 3 Due on Sunday November 29th
- Exercise sheet 4 Due on Sunday December 6th
- Exercise sheet 5 Due on Sunday December 13th
- Exercise sheet 6 Due on Sunday December 20th
- Exercise sheet 7 Due on Tuesday January 19th
- Exercise sheet 8 Due on Sunday January 24th
- Exercise sheet 9 Due on Sunday January 31st
Literature
- Adams, John Frank. Stable homotopy and generalised homology. University of Chicago press, 1974.
- Segal, Graeme. "Categories and cohomology theories" Topology 13.3 (1974): 293-312.
- Schwede, Stefan. Symmetric spectra, in preparation, online version accessible at the author's webpage. (2012).
- Lurie, Jacob. Higher Algebra, available at the author's webpage (September 2017).