• Corpus ID: 235683287

Configuration spaces of clusters as $E_d$-algebras

@inproceedings{Kranhold2021ConfigurationSO,
  title={Configuration spaces of clusters as \$E\_d\$-algebras},
  author={Florian Kranhold},
  year={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 suspension of the labelling space. The aim of this paper is to study a variation of these spaces, namely the configuration space of labelled clusters of points in Rd. This configuration space is again an Ed-algebra, but in general not a free one. We give geometric models for their iterated bar… 
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References

SHOWING 1-10 OF 27 REFERENCES
Vertical configuration spaces and their homology
We introduce ordered and unordered configuration spaces of ‘clusters’ of points in an Euclidean space R d , where points in each cluster satisfy a ‘verticality’ condition, depending on a decomposition
$E_2$-cells and mapping class groups
We prove a new kind of stabilisation result, "secondary homological stability", for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained
Higher genus surface operad detects infinite loop spaces
Abstract. The operad studied in conformal field theory and introduced ten years ago by G. Segal [S] is built out of moduli spaces of Riemann surfaces. We show here that this operad which at first
Classifying Spaces of Topological Monoids and Categories
0. Introduction. In recent years, a number of curious and seemingly paradoxical properties of the bar constuction have come to light. These results have the general form that, in certain situations,
...
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