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The operad structure of admissible G-covers
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2013 (English)In: Algebra & Number Theory, ISSN 1937-0652, Vol. 7, no 8, 1953-1975 p.Article in journal (Refereed) Published
Abstract [en]

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 [X/G] give examples of G-CohFTs.

Place, publisher, year, edition, pages
2013. Vol. 7, no 8, 1953-1975 p.
Keyword [en]
Cohomological field theory, Modular operad, Operad colored by groupoid, Orbifold Gromov-Witten theory
National Category
URN: urn:nbn:se:kth:diva-139453DOI: 10.2140/ant.2013.7.1953ISI: 000329706400007ScopusID: 2-s2.0-84889037005OAI: diva2:687662

QC 20140115

Available from: 2014-01-15 Created: 2014-01-13 Last updated: 2014-02-07Bibliographically approved

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Petersen, Dan
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