Abstract
Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy quotient we build an aspherical topological operad that we call the little bundles operad. As our main result, we describe this operad as a groupoid-valued operad in terms of generators and relations and prove that the categorical little bundles algebras are precisely braided –crossed categories in the sense of Turaev. Moreover, we prove that the evaluation on the circle of a homotopical two-dimensional equivariant topological field theory yields a little bundles algebra up to coherent homotopy.
Citation
Lukas Müller. Lukas Woike. "The little bundles operad." Algebr. Geom. Topol. 20 (4) 2029 - 2070, 2020. https://doi.org/10.2140/agt.2020.20.2029
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