On the Takayasu cofibre sequences

Nom de l'orateur
Nguyễn Đặng Hồ Hải
Etablissement de l'orateur
Université de Hué (Vietnam)
Date et heure de l'exposé
Lieu de l'exposé
Salle Eole

Given two natural numbers n and k, consider the Thom space over the classifying space of a rank n elementary abelian 2-group associated to k copies of its real reduced regular representation. The Steinberg module of the general linear group gives rise to a stable summand of this Thom space, denoted by $L(n,k)$. Takayasu (1999) showed the existence of a cofibre sequences $$\Sigma^kL(n-1,2k+1) \to L(n,k) \to L(n,k+1),$$ which generalizes the stable splitting of Mitchell and Priddy. A cofiber sequence of the same form was proved by Arone and Mahowald by combining Goodwillie calculus with the James fibration.

I will describe in this talk how to derive the existence of the above cofibre sequences from the vanishing of some extension groups in the category of modules over the mod 2 Steenrod algebra.
This is joint work with Lionel Schwartz.