Mandell's Theorem
Goal of the project
The goal of this project is to understand the following theorems of Mandell:
Theorem 1: Two finite p-type nilpotent p-complete spaces X and Y are of the same p-type if and only if the E∞-algebra of singular cochains with Fp coefficients are quasi-isomorphic as E∞-algebras.
Theorem 2 (a stronger statement): Two finite type nilpotent spaces X and Y are weakly equivalent and only if the E∞-algebra of singular cochains with Z coefficients are quasi-isomorphic as E∞-algebras.
Schedule (for March)
8 March: Introduction (Joana) - Notes
15 March: Operads (Bashar) - Notes
22 March: Examples of interesting CW complexes (Carles) - Notes
12 April: E∞-algebras (Bashar)
19 April: Steenrod operations (Anna) - Notes
26 April: Overview of rational homotopy theory (Roger) - Notes
3 May: E∞-algebra structure on C*sing(X) (César) -Notes
10 May: Quillen model structures and Quillen equivalences (Javier)
17 May: Homotopy theory of E∞-algebras (Javier)
26 May: p-adic model structure on simplicial sets (David) - Notes
31 May: Postnikov towers for p-complete spaces (Nathan)
7 June: Resolvable spaces (Bashar)
Proof of Mandell's theorems