Abstract

We construct a two-level weighted topological quantum field theory whose structure coeficients are equivariant intersection numbers on moduli spaces of admissible covers. Such a structure is parallel (and strictly related) to the local Gromov–Witten theory of curves of Bryan and Pandharipande. We compute explicitly the theory using techniques of localization on moduli spaces of admissible covers of a parametrized P¹. The Frobenius algebras we obtain are one-parameter deformations of the class algebra of the symmetric group S_d. In certain special cases we are able to produce explicit closed formulas for such deformations in terms of the representation theory of S_d.

Keywords

TQFT, topological quantum field theory, admissible covers, Gromov–Witten Invariants

Mathematical Subject Classification

Primary: 14N35

Authors