Getzler relation and Virasoro conjecture for genus one

Abstract

We derive explicit universal equations for primary Gromov-Witten invariants by applying Getzler's genus one relation to quantum powers of Euler vector field. As an application, we provide some evidences for the genus-1 Virasoro conjecture.

References in corpus (5)

• The structure of 2D semi-simple field theories
• Quantum Cohomology and Virasoro Algebra
• Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
• Constraints For Topological Strings In $D\ge 1$
• Elliptic Gromov-Witten Invariants And Virasoro Conjecture