arXiv subjects
Publications and source records attributed to Safia Chettih.
We show that normalized cacti form an $\infty$-operad in the form of a dendroidal space satisfying a weak Segal condition. To do this, we introduce a new topological operad of bracketed trees and an enrichment of the dendroidal category $Ω$.
We show that the homology of ordered configuration spaces of finite trees with loops is torsion free. We introduce configuration spaces with sinks, which allow for taking quotients of the base space. Furthermore, we give a concrete generating set for all homology groups of configuration spaces of trees with loops and the first homology group of configuration spaces of general finite graphs. An important technique in the paper is the identification of the $E^1$-page and differentials of Mayer-Vietoris spectral sequences for configuration spaces.