Equivariant Gromov-Witten invariants

摘要: The objective of this paper is to describe some construction and applications the equivariant counterpart Gromov-Witten (GW) theory, i.e. intersection theory on spaces (pseudo-) holomorphic curves in (almost-) Kahler manifolds. Given a Killing action compact Lie group G manifold X, GW-theory provides, as we will show Section 3, cohomology space H G(X) with Frobenius structure (see [2]). We discuss computation ([7],[11]) quantum algebras flag manifolds (Section 5), simultaneous diagonalization cup-product operators (Sections 7,8), S-equivariant Floer homology loop LX 6 [10],[9]) “quantum” version Serre duality theorem 12). In Sections 9 — 11 combine general developed 1 fixed point localization technique [3] order prove mirror conjecture (in form suggested [10]) for projective complete intersections. By one usually means intriguing relations (discovered by physicists) between symplectic complex geometry Calabi–Yau nfold respectively another Calabi-Yau n-fold called partner former one. remakable application [16] enumeration rational 3-folds (1991, see below) raised number new mathematical problems challenging maturity tests modern methods topology.