Vertical configuration spaces and their homology

Abstract

We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space ${\mathbb{R}}^d$, where points in each cluster satisfy a 'verticality' condition, depending on a decomposition $d=p+q$. We compute the homology in the ordered case and prove homological stability in the unordered case.

29 pages, 9 figures; accepted version

References in corpus (1)

• Homological stability for subgroups of surface braid groups

Cited by in corpus (1)

• Configuration spaces of clusters as $E_d$-algebras