These are some notes on Thom spectra, placed within the context of the six-functor formalism of parametrised spectra. They are based on a Chinese version on 香蕉空间 that I drafted during the summer of 2025, which I translated to English and expanded quite a bit around December. There was a TeXed up Chinese version before the content expansion, which I might make public after backporting the changes (when I have time and remember).
UPDATES:
- (20.apr.2026) Fixed a few typos. Minor changes in 1.2 following feedback from Bastiaan Cnossen.
The ideas are mostly based on the work of Ando–Blumberg–Gepner–Hopkins–Rezk. I should mention the work of Antolín-Camarena–Barthel as well, which hasn't come up in the notes. The notes are more centered around the use of six-functors for classical algebraic topology.
The current notes have been distributed within our working groups and to a few fellow students, but not more broadly than that, as I have hesitations about conducting much academic activity under my current legal identity, especially on the internet.