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2020 The little bundles operad
Lukas Müller, Lukas Woike
Algebr. Geom. Topol. 20(4): 2029-2070 (2020). DOI: 10.2140/agt.2020.20.2029

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.

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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

Information

Received: 12 March 2019; Revised: 21 September 2019; Accepted: 1 October 2019; Published: 2020
First available in Project Euclid: 1 August 2020

zbMATH: 07226710
MathSciNet: MR4127089
Digital Object Identifier: 10.2140/agt.2020.20.2029

Subjects:
Primary: 18D50
Secondary: 18D10, 57R56

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 4 • 2020
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