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 …

Let A be an associative ring and M a finitely generated projective A-module. We introduce a
category RBS (M) and prove several theorems which show that its geometric realisation …

Using the language of twisted skew-commutative algebras, we define secondary
representation stability, a stability pattern in the unstable homology of spaces that are …

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

We prove a new kind of stabilisation result,“secondary homological stability,” for the
homology of mapping class groups of orientable surfaces with one boundary component …

We prove new homological stability results for general linear groups over finite fields. These
results are obtained by constructing CW approximations to the classifying spaces of these …

Given an $ E_1 $-ring $ A $ and a class $ a\in\pi_ {mk}(A) $ satisfying a suitable hypothesis,
we define a map of $ E_1 $-rings $ A\to A (\sqrt [m]{a}) $ realizing the adjunction of an $ m …

We investigate stability properties of the reductive Borel-Serre categories; these were
introduced as a model for unstable algebraic K-theory in previous work. We see that they …

We show that the Iwahori–Hecke algebras H n H_n of type A n− 1 A_n-1 satisfy homological
stability, where homology is interpreted as an appropriate Tor group. Our result precisely …

We prove a general homological stability theorem for certain families of groups equipped
with product maps, followed by two theorems of a new kind that give information about the …