Permutation-equivariant quantum K-theory I. Definitions. Elementary K-theory of ${\overline{\mathcal{M}}}_{0,n}/S_n$

Abstract

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 $S_n$-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 $S_n$ 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 ${\overline{\mathcal{M}}}_{0,n}$.

9 pages, 1 figure

Cited by in corpus (2)

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