Open Access
Translator Disclaimer
2013 The operad structure of admissible $G$-covers
Dan Petersen
Algebra Number Theory 7(8): 1953-1975 (2013). DOI: 10.2140/ant.2013.7.1953


We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible G-cover. To do this we are forced to introduce the notion of an operad colored not by a set but by the objects of a category. This construction interpolates in a sense between “framed” and “colored” versions of operads; we hope that it will be of independent interest. An algebra over the cohomology of this operad is the same thing as a G-equivariant CohFT, as defined by Jarvis, Kaufmann and Kimura. We prove that the (orbifold) Gromov–Witten invariants of global quotients [XG] give examples of G-CohFTs.


Download Citation

Dan Petersen. "The operad structure of admissible $G$-covers." Algebra Number Theory 7 (8) 1953 - 1975, 2013.


Received: 4 June 2012; Revised: 18 January 2013; Accepted: 16 March 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1305.18037
MathSciNet: MR3134040
Digital Object Identifier: 10.2140/ant.2013.7.1953

Primary: 18D50
Secondary: 14D21 , 14H10

Keywords: cohomological field theory , modular operad , operad colored by groupoid , orbifold Gromov–Witten theory

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.7 • No. 8 • 2013
Back to Top