Pointed admissible G-covers and G-equivariant cohomological field theories

By Tyler Jarvis, R. Kaufmann, T. Kimura. Compositio Mathematica, 2003

52 citations recorded by the source corpus.

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 $[X/G]$ as well as the ring $H^{\bullet}(X,G)$ of Fantechi and Göttsche.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/35713856868b50cd4f1796ffa765357c1a4197ed

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In Geometry and Topology

  1. K. Costello
  2. D. Shklyarov
  3. Luc Menichi
  4. Jacob Lurie
  5. D. Abramovich
  6. Jonathan Wise
  7. G. Moore
  8. G. Segal

In Mathematical Physics

  1. K. Costello
  2. D. Shklyarov
  3. Luc Menichi
  4. Jacob Lurie
  5. G. Moore
  6. J. Francis
  7. G. Segal
  8. David Ayala

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