A formula for the total permutation-equivariant K-theoretic Gromov-Witten potential

TL;DR

This paper presents a combinatorial formula for the permutation-equivariant K-theoretic Gromov-Witten potential of a projective manifold, linking it to cohomological GW invariants via Kawasaki strata analysis.

Contribution

It introduces a graph-summation formula that expresses the K-theoretic GW potential in terms of cohomological invariants, providing a new computational approach.

Findings

Derived a summation over graphs formula for K-theoretic GW potential

Connected Kawasaki strata of moduli spaces to combinatorial structures

Facilitated computation of permutation-equivariant GW invariants

Abstract

We give a summation over graphs type formula for the permutation-equivariant K-theoretic Gromov-Witten total potential of a projective manifold X in terms of cohomological Gromov-Witten (GW) invariants of X. We achieve this by describing combinatorially the Kawasaki strata of the moduli spaces of stable maps to X.