GdT : Stabilité homologique via les E_k-algèbres cellulaires

List of talks

• Talk 0 (01/10/2024): Présentation. | Ricardo Campos. Notes par Ricardo
• Talk 1 (15/10/2024): Filtered, cellular and CW algebras; skeletal filtration and the associated graded [C; §5, §6 (thm 6.14)]. Model structures on operads and algebras [C; §9]. | Mario Fuentes. Notes par Mario, Ricardo.
• Talk 1.5 (05/11/2024): Continuation. Notes par Ricardo.
• Talk 2 (12/11/2024): Ek-algebras in sSet, (derived ) indecomposables [L; §2]. | Joost Nuiten. Notes par Mario, Joan.
• Talk 3 (26/11/2024): The homology of free Ek-algebras [L; §4]. | Joan Millès
• Talk 4: More indecomposables, connectivity, Hurewicz and Whitehead theorems, CW approximation [L; §5], see also [C; §11].
• Talk 5(+6?): Classical facts about mapping class groups [L;3, 6]. [MCG] isn't yet too pertinent but worth looking at.
• Talk 7: Generic Homological Stability I [L; §8].
• Talk 8: Generic Homological Stability II [L; §9].
• Talk 9: Generic Homological Stability III [L; §10].
• Talk 10: Secondary Homological stability over Q (optional: over Z) [L; §11].
• Talk 11: Other applications such as homology of the E_\infty algebra \sqcap_n BGL_n(Fp) [Fp].

References

• [L] Lecture notes: Lecture notes on Cellular Ek-algebras
• [C] All the theory: Cellular Ek-algebras
• [MCG] Applications to mapping class groups: E2-cells and mapping class groups
• [Fp] Applications to GLn(Fp): E∞-cells and general linear groups of finite fields