Configuration spaces of algebraic varieties

FI-modules were introduced by the first three authors in [CEF] to encode sequences of representations of symmetric groups. Over a field of characteristic 0, finite generation of an FI-module implies representation stability for the corresponding sequence of S nrepresentations. In this paper we prove the Noetherian property for FI-modules over arbitrary Noetherian rings: any sub-FI-module of a finitely-generated FI-module is finitely generated. This lets us extend many of the results of [CEF] to representations in positive characteristic, and even to integral coefficients. We focus on three major applications of the main theorem: on the integral and mod p cohomology of configuration spaces; on diagonal coinvariant algebras in positive characteristic; and on an integral version of Putman's central stability for homology of congruence subgroups.

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“…Totaro describes the E 2 page of this spectral sequence [T,Theorem 1], and in particular he shows that E…”

Section: Configuration Co-fi-spaces (Proof Of Theorem E)mentioning

confidence: 99%

FI-modules over Noetherian rings

et al. 2014

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“…We [2]. For such a projective manifold M, Fulton-Mac Pherson [4] and Kriz [7] have given an explicit CDGA model for the configuration space F(M, k), for any k (see also [13] is the element such that w (~C) = 1. Thus A is a shriek map in the sense of Definition 3.1 in [9].…”

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confidence: 99%

The rational homotopy type of configuration spaces of two points

Lambrechts¹,

Stanley²

2004

Annales De L’institut Fourier

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“…We give two examples using this theorem. Theses examples are interesting to compare since the Lens spaces L (11,2) and L (11,3) are the smallest Lens spaces that both admit non-trivial Massey products and are homotopy equivalent but not homeomorphic. The tables below describe only the non-empty intersections (A 1+ X 1,1+ ) using the following conventions: if an entry is blank the intersection is empty, and a list of numbers, i 1 , .…”

Section: Proposition 331 When J Is Q-covering and ∈ Z P Thenmentioning

confidence: 99%

“…Configuration spaces have played an important role in many areas of topology, ranging from operads to iterated loop spaces to knot theory. They have also been studied for their own sake, and in general it is not known how to compute the cohomology ring of configurations in an arbitrary manifold, see Bendersky and Gitler [3], Cohen and Taylor [4], Felix and Thomas [5], and Totaro [11].…”

Section: Configuration Spacesmentioning

confidence: 99%

Rational homotopy models for two-point configuration spaces of lens spaces

Miller

2011

Homology, Homotopy and Applications

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We study the algebraic topology of configuration spaces as interesting objects in their own right and with the goal of constructing invariants for topological manifolds. We calculate the complete Massey product structure for the universal cover of the space of two point configurations in a three-dimensional lens space. We then construct rational homotopy models for these spaces and calculate the rational homotopy groups.

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Configuration spaces of algebraic varieties

Cited by 151 publications

References 8 publications

FI-modules over Noetherian rings

FI-modules over Noetherian rings

The rational homotopy type of configuration spaces of two points

Rational homotopy models for two-point configuration spaces of lens spaces

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