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The little bundles
operad
Lukas Müller and Lukas Woike |
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Algebraic & Geometric Topology 20 (2020) 2029–2070
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Abstract |
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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. |
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Keywords
operad, topological field theory, braid group, monoidal
category, braided monoidal category
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Mathematical Subject Classification 2010
Primary: 18D50
Secondary: 18D10, 57R56
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References |
Publication
Received: 12 March 2019
Revised: 21 September 2019
Accepted: 1 October 2019
Published: 20 July 2020
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Authors |
| Lukas Müller | |
| Department of Mathematics Heriot-Watt University Edinburgh United Kingdom |
Maxwell Institute for Mathematical
Sciences Edinburgh United Kingdom |
| Lukas Woike | |
| Fachbereich Mathematik Universität Hamburg Hamburg Germany |
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