Vol. 1, No. 1, 2007

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A topological quantum field theory of intersection numbers on moduli spaces of admissible covers

Renzo Cavalieri

Vol. 1 (2007), No. 1, 35–66

We construct a two-level weighted topological quantum field theory whose structure coefficients 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 1. The Frobenius algebras we obtain are one-parameter deformations of the class algebra of the symmetric group Sd. In certain special cases we are able to produce explicit closed formulas for such deformations in terms of the representation theory of Sd.

TQFT, topological quantum field theory, admissible covers, Gromov–Witten Invariants
Mathematical Subject Classification 2000
Primary: 14N35
Received: 10 February 2007
Accepted: 13 May 2007
Published: 1 February 2007
Renzo Cavalieri
University of Michigan
Department of Mathematics
2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States