Homological stability for coloured configuration spaces and symmetric complements

Abstract

We prove a homological stability theorem for certain complements of symmetric spaces. This is a variant of a conjecture by Vakil and Matchett Wood for subspaces of ${\mathrm{Sym}}^n(X)$ where $X$ is an open manifold admitting a boundary. To do this we prove a homological stability result for a type of "coloured" configuration space by adding points of the same colour.

12 pages

References in corpus (2)

• Discriminants in the Grothendieck Ring
• Homological stability for complements of closures

Cited by in corpus (2)

• Discriminants in the Grothendieck Ring
• Plant complexes and homological stability for Hurwitz spaces