Reduced genus-one gromov-witten invariants

In a previous paper, we described a natural closed subset, 𝔐¯_{1, k} ⁰(X, A;J), of the moduli space 𝔐¯_{1, k}(X, A;J) of stable genusone J-holomorphic maps into a symplectic manifold X. In this paper we generalize the definition of the main component to moduli spaces of perturbed, in a restricted way, J-holomorphic maps and conclude that 𝔐¯_{1, k} ⁰(X, A;J), just like 𝔐¯_{1, k}(X, A;J), carries a virtual fundamental class, which can be used to define symplectic invariants. These truly genus-one invariants constitute part of the standard genus-one Gromov-Witten invariants, which arise from the entire moduli space 𝔐¯_{1, k}(X, A;J). The new invariants are more geometric and can be used to compute the genus-one GW-invariants of complete intersections, as shown in a separate paper.