The little bundles operad

Lukas Müller, Lukas Woike

Research output: Contribution to journalArticle

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 G –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.

Original languageEnglish
Pages (from-to)2029-2070
Number of pages42
JournalAlgebraic and Geometric Topology
Volume20
Issue number4
DOIs
Publication statusPublished - 20 Jul 2020

ASJC Scopus subject areas

  • Geometry and Topology

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