Abstract
We give a direct combinatorial proof that the modular envelope of the cyclic operad \(\mathcal {A} ss \) is the modular operad of (the homeomorphism classes of) 2D compact surfaces with boundary with marked points.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chuang, J., Lazarev, A.: Dual Feynman transform for modular operads. Commun. Number Theory Phys. 1(4), 605–649 (2007). arXiv:0704.2561v2 [math.QA]
Costello, K.: The A-infinity operad and the moduli space of curves, February 2004, arXiv:math/0402015 [math.AG]
Doubek, M., Jurčo, B., Münster, K.: Modular operads and the quantum open–closed homotopy algebras. J. High Energy Phys. 2015, 158 (2015). arXiv:1308.3223v2 [math.AT]
Giansiracusa, J.: The framed little 2-discs operad and diffeomorphisms of handlebodies. J. Topol. 4(4), 919–941 (2011). arXiv:1008.3272v2 [math.GT]
Markl, M.: Loop homotopy algebras in closed string field theory. Commun. Math. Phys. 221, 367–384 (2001). arXiv:hep-th/9711045v2
Author information
Authors and Affiliations
Additional information
The author was supported by GAČR 201/12/G028 at the initial stage of the project and by GAČR P201/13/27340P at the later stage.
Rights and permissions
About this article
Cite this article
Doubek, M. The Modular Envelope of the Cyclic Operad \(\mathcal {A} ss \) . Appl Categor Struct 25, 1187–1198 (2017). https://doi.org/10.1007/s10485-017-9491-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10485-017-9491-1