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Galois actions on surfaces and a higher genus Grothendieck-Teichmüller group
Luciana Basualdo Bonatto, Marcy Robertson
We construct a modular operad of mapping class groupoids modelling the higher-genus Teichmüller tower, with compositions and contractions encoding surface gluing. We p…
Decoupling generalised configuration spaces on surfaces
Luciana Basualdo Bonatto
The configuration space of k points on a manifold carries an action of its diffeomorphism group. The homotopy quotient of this action is equivalent to the classifying space of diff…
Decoupling decorations on moduli spaces of manifolds
Luciana Basualdo Bonatto
We consider moduli spaces of -dimensional manifolds with embedded particles and discs. In this moduli space, the location of the particles and discs is constrained by the -di…
An infinity operad of normalized cacti
Luciana Basualdo Bonatto, Safia Chettih, Abigail Linton +3
We show that normalized cacti form an -operad in the form of a dendroidal space satisfying a weak Segal condition. To do this, we introduce a new topological operad of brac…