Permutation-equivariant quantum K-theory I. Definitions. Elementary K-theory of M₀,ₙ/Sₙ

الأصل · EN

K-theoretic Gromov-Witten invariants of a compact Kahler manifold X are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. With this article, we begin a series of publications on K-theoretic Gromov-Witten invariants, cognizant of the Sₙ-module structure on the sheaf cohomology, induced by renumbering of the marked points. In the opening paper, we introduce such invariants, explain how the representation-theoretic information with varying Sₙ is incorporated into generating functions of Gromov-Witten theory, and compute one of them, the small J-function for X=pt, by using Kapranov's description of Deligne-Mumford spaces M₀,ₙ.