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Moscow Mathematical Journal

Volume 17, Issue 4, October–December 2017  pp. 691–698.

Permutation-Equivariant Quantum K-Theory I. Definitions. Elementary K-Theory of \overline M0,n/Sn

Authors:  Alexander Givental (1)
Author institution:(1) Department of Mathematics, University of California Berkeley, Berkeley CA 94720, USA


K-theoretic Gromov–Witten (GW) invariants of a compact Kähler manifold X are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. In this paper, we introduce K-theoretic GW-invariants cognizant of the Sn-module structure on the sheaf cohomology, induced by renumbering of the marked points, and compute some of these invariants for X=pt.

2010 Math. Subj. Class. 14N35.

Keywords: K-theory, Gromov–Witten invariants, Schur–Weyl reciprocity, Deligne–Mumford spaces, Veronese curves.

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