# Vertical configuration spaces and their homology

@inproceedings{Bianchi2021VerticalCS, title={Vertical configuration spaces and their homology}, author={Andrea Bianchi and Florian Kranhold}, year={2021} }

We introduce ordered and unordered configuration spaces of ‘clusters’ of points in an Euclidean space Rd, 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.

#### 2 Citations

Configuration spaces of clusters as $E_d$-algebras

- Mathematics
- 2021

It is a classical result that configuration spaces of labelled particles in Rd are free algebras over the little d-cubes operad Cd, and their d-fold bar construction is equivalent to the d-fold… Expand

Splittings and deloopings of vertical configuration spaces

- 2021

We introduce a labelled version of the configuration spaces V(Rp,q) of vertically aligned clusters and prove a stable splitting result for them. On the other hand, these spaces turn out to be… Expand

#### References

SHOWING 1-10 OF 17 REFERENCES

Splittings and deloopings of vertical configuration spaces

- 2021

We introduce a labelled version of the configuration spaces V(Rp,q) of vertically aligned clusters and prove a stable splitting result for them. On the other hand, these spaces turn out to be… Expand

Homological stability for moduli spaces of disconnected submanifolds, I

- Mathematics
- 2018

A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to… Expand

(Non-)formality of the extended Swiss Cheese operads

- Mathematics
- 2017

We study two colored operads of configurations of little $n$-disks in a unit $n$-disk, with the centers of the small disks of one color restricted to an $m$-plane, $m<n$. We compute the rational… Expand

Vertical configuration spaces and homological stability

- Master’s thesis. Rheinische Friedrich-Wilhelms-Universität Bonn,
- 2017

Vertical configuration spaces and homological stability'. Master's thesis

- 2017

Homological stability for Hurwitz spaces

- PhD thesis. Gottfried Wilhelm Leibniz Universität Hannover,
- 2016

Homological stability for Hurwitz spaces'. Dissertation

- 2016

Homological stability for subgroups of surface braid groups

- Mathematics
- 2014

In this paper we prove homological stability for certain subgroups of surface braid groups. Alternatively, this is equivalent to proving homological stability for configurations of subsets of exactly… Expand

The (non-equivariant) homology of the little disks operad

- In: Séminaires et Congrès
- 2013

Twisted homological stability for configuration spaces

- Mathematics
- 2013

Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with… Expand