Geodesic
Configuration spaces of clusters as $E_d$-algebras
Homology, homotopy, and applications, Tome 26 (2024) no. 1, pp. 319-339.

Voir la notice de l'article provenant de la source International Press of Boston

It is a classical result that configuration spaces of labelled particles in $\mathbb{R}^d$ are free $E_d$-algebras and that their $d$-fold bar construction is equivalent to the $d$-fold suspension of the labelling space. In this paper, we study a variation of these spaces, namely configuration spaces of labelled clusters of particles. These configuration spaces are again $E_d$-algebras, and we give geometric models for their iterated bar construction in two different ways: one establishes a description of these configuration spaces of clusters as cellular $E_1$-algebras, and the other one uses an additional verticality constraint. In the last section, we apply these results in order to calculate the stable homology of certain vertical configuration spaces.
DOI : 10.4310/HHA.2024.v26.n1.a19
Classification : 55P35, 55P48, 55P65, 55R80, 57T30
Keywords: configuration space, $E_d$-algebra, bar construction, stable homology 
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     author = {Florian Kranhold},
     title = {Configuration spaces of clusters as $E_d$-algebras},
     journal = {Homology, homotopy, and applications},
     pages = {319--339},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n1.a19/}
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Florian Kranhold. Configuration spaces of clusters as $E_d$-algebras. Homology, homotopy, and applications, Tome 26 (2024) no. 1, pp. 319-339. doi : 10.4310/HHA.2024.v26.n1.a19. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n1.a19/

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