Lecture Notes

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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)

Course Info

As Taught In
Fall 2007
Learning Resource Types
Lecture Notes