On the operad structure of admissible G-covers
(English)Manuscript (preprint) (Other academic)
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 groupoid. This construction interpolates in some sense between “framed” and “colored” versions of operads; we hope that it will be of independent interest. An algebra over this operad is the same thing as a G-equivariant CohFT. Our main theorem is an extension of the symmetric function formalism for modular operads to this setting; we prove an analogue of the formula of Getzler and Kapranov describing the effect of the “free modular operad” functor on the level of symmetric functions.
Algebra and Logic
IdentifiersURN: urn:nbn:se:kth:diva-48902OAI: oai:DiVA.org:kth-48902DiVA: diva2:458839
QS 20112011-11-242011-11-242013-05-20Bibliographically approved