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Lecture notes files.
| LEC # |
TOPICS |
| 1 |
Introduction (PDF) |
| 2 |
Steenrod operations (PDF) |
| 3 |
Basic properties of Steenrod operations (PDF) |
| 4 |
The Adem relations (PDF) |
| 5 |
The Adem relations (cont.) (PDF) |
| 6 |
Admissible monomials (PDF) |
| 7 |
Free unstable modules (PDF) |
| 8 |
A theorem of Gabriel-Kuhn-Popesco (PDF) |
| 9 |
Injectivity of the cohomology of BV (PDF) |
| 10 |
Generating analytic functors (PDF) |
| 11 |
Tensor products and algebras (PDF) |
| 12 |
Free unstable algebras (PDF) |
| 13 |
The dual Steenrod algebra (PDF) |
| 14 |
The Frobenius (PDF) |
| 15 |
Finiteness conditions (PDF) |
| 16 |
Some unstable injectives (PDF) |
| 17 |
Injectivity of tensor products (PDF) |
| 18 |
Lannes' T-functor (PDF) |
| 19 |
Properties of T (PDF) |
| 20 |
The T-functor and unstable algebras (PDF) |
| 21 |
Free E-infinity algebras (PDF) |
| 22 |
A pushout square (PDF) |
| 23 |
The Eilenberg-Moore spectral sequence (PDF) |
| 24 |
Operations on E-infinity algebras (PDF) |
| 25 |
T and the cohomology of spaces (PDF) |
| 26 |
Profinite spaces (PDF) |
| 27 |
p-adic homotopy theory (PDF) |
| 28 |
Atomicity (PDF) |
| 29 |
Atomicity of connected p-Finite spaces (PDF) |
| 30 |
The Sullivan conjecture (PDF) |
| 31 |
p-Profinite completion of spaces (PDF) |
| 32 |
The arithmetic square (PDF) |
| 33 |
The Sullivan conjecture revisited (PDF) |
| 34 |
Quaternionic projective space (PDF) |
| 35 |
Analytic functors revisited (PDF) |
| 36 |
The Nil-filtration (PDF) |
| 37 |
The Krull filtration (PDF) |
| 38 |
Epilogue (PDF) |
