2003/02/28 by Tyler J. Jarvis, Ralph M. Kaufmann, Ralph Kaufmann +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #math.QA #msc:14N35 #msc:53D45
paper · pdf · doi:10.1112/s0010437x05001284
published as Compositio Mathematica 141 (2005) 926-978 · Corrected proof of the trace axiom and made minor typo corrections. 13 figures. Uses Paul Taylor's diagrams package
arxiv created 2005/06/09 · openalex publication_date 2005/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduces to the moduli space of stable curves and a cohomological field theory (CohFT), respectively. We prove that taking the ‘quotient’ by G reduces a G-CohFT to a CohFT. We also prove that a G-CohFT contains a G-Frobenius algebra, a G-equivariant generalization of a Frobenius algebra, and that the ‘quotient’ by G agrees with the obvious Frobenius algebra structure on the space of G-invariants, after rescaling the metric. We then introduce the moduli space of G-stable maps into a smooth, projective variety X with G action. Gromov–Witten-like invariants of these spaces provide the primary source of examples of G-CohFTs. Finally, we explain how these constructions generalize (and unify) the Chen–Ruan orbifold Gromov–Witten invariants of of Fantechi and Göttsche.