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A TQFT of Intersection Numbers on Moduli Spaces of Admissible Covers

Renzo Cavalieri
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Abstract

We construct a two-level weighted TQFT whose structure coefficents 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-Pandharipande. We compute explicitly the theory using techniques of localization on moduli spaces of admissible covers of a parametrized projective line. 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.

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Renzo Cavalieri. 2005-12-11. A TQFT of Intersection Numbers on Moduli Spaces of Admissible Covers. https://arxiv.org/abs/math/0512225

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