This is the webpage for my personal study (“project”) on the Kervaire invariant one problem. I am also aiming to complete a systematic study of Adams spectral sequence.
This “project” is designed in two parts: Adams spectral sequence, and the rest, i.e. the proof aimed at the main theorem, which is supposed to contain: slice spectral sequence, the 
-spectrum 
, and the three theorems (the gap theorem, the periodicity theorem and the detection theorem).
Prerequisites:
- Equivariant stable homotopy theory.
- This is standard. I strongly recommend Dr. Ramzi’s notes, which is in a flavour of higher categories.
- Certainly, we have other standard materials. As references, I would like to recommend Prof. Schwede’s notes or Chapter 17 by Prof. Mike Hill in Handbook of Homotopy Theory.
- Adams Spectral Sequence.
- Indeed this topic overlaps partly with the Kervaire invariant one problem, but I aim to include it in this “project” as well.
Record:
To be updated.
References (to be continued):
- General References:
- Original paper by Hill–Hopkins–Ravenel: publised version, arxiv version.
- Ravenel’s Kervaire invariant page.
- The purple book by Hill–Hopkins–Ravenel.
- A seminar on Kervaire invariant at Stockholm University.
- References on the equivariant stable homotopy theory:
- Dr. Ramzi’s notes.
- Chapter 17 by Prof. Mike Hill in Handbook of Homotopy Theory.
- Prof. Schwede’s notes.
- References on Adams spectral sequence:
- Syllabus of a seminar at Bonn University.
- Notes by Prof. Rognes.
- Standard textbook by Prof. Ravenel.