We study analogues of FI-modules where the role of the symmetric group is played by the
general linear groups and the symplectic groups over finite rings, and we prove basic …

We prove a homological stability theorem for families of discrete groups (eg mapping class
groups, automorphism groups of free groups, braid groups) with coefficients in a sequence …

We compute the stable homology of the braid group with coefficients in any Schur functor
applied to the integral reduced Burau representation. This may be considered as a …

We give a set of foundations for cellular $ E_k $-algebras which are especially convenient
for applications to homological stability. We provide conceptual and computational tools in …

We prove a version of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics for Selmer
groups of quadratic twist families of abelian varieties over global function fields. As a …

An FI-module V over a commutative ring K encodes a sequence (V n) n≥ 0 of
representations of the symmetric groups (G n) n≥ 0 over K. We show that for a" finitely …

We determine $\pi _*(B\operatorname {Diff} _\partial (D^{2n}))\otimes\mathbb {Q} $ for $2
n\geq 6$ completely in degrees $*\leq 4n-10$, far beyond the pseudoisotopy stable range …

Given a graded E 1–module over an E 2–algebra in spaces, we construct an augmented
semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution …

Improved homological stability for certain general linear groups - Kupers - 2022 -
Proceedings of the London Mathematical Society - Wiley Online Library Skip to Article …

Homological stability for sequences G n→ G n+ 1→⋯ of groups is often proved by studying
the spectral sequence associated to the action of G n on a highly connected simplicial …