In this paper we introduce and develop the theory of FI-modules. We apply this theory to
obtain new theorems about:• the cohomology of the configuration space of n distinct ordered …

Given a category $\mathcal {C} $ of a combinatorial nature, we study the following
fundamental question: how do combinatorial properties of $\mathcal {C} $ affect algebraic …

Given a family of groups admitting a braided monoidal structure (satisfying mild
assumptions) we construct a family of spaces on which the groups act and whose …

FI-modules were introduced by the first three authors to encode sequences of
representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI …

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 develop a comprehensive theory of the stable representation categories of several
sequences of groups, including the classical and symmetric groups, and their relation to the …

Let C n (M) be the configuration space of n distinct ordered points in M. We prove that if M is
any connected orientable manifold (closed or open), the homology groups H i (C n (M); ℚ) …

Consider the polynomial ring in countably infinitely many variables over a field of
characteristic zero, together with its natural action of the infinite general linear group $ G …

This article is a sequel to [14]. We study a space g, n of genus g stable, n-marked tropical
curves with total edge length 1. Its rational homology is identified with both top-weight …

Torelli groups are subgroups of map** class groups that consist of those diffeomorphism
classes that act trivially on the homology of the associated closed surface. The Johnson …