A reconstruction theorem expresses genus-one permutation-equivariant quantum K-invariants of any compact Kähler manifold in terms of genus-zero data and residues.
Permutation-equivariant quantum K-theory VII. General theory
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abstract
We introduce K-theoretic GW-invariants of mixed nature: permutation-equivariant in some of the inputs and ordinary in the others, and prove the ancestor-descendant correspondence formula. In genus 0, combining this with adelic characterization, we derive that the range ${\mathcal L}_X$ of the big J-function in permutation-equivariant theory of a target space $X$ is overruled.
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Reconstruction of $g=1$ permutation equivariant quantum $K$-invariants
A reconstruction theorem expresses genus-one permutation-equivariant quantum K-invariants of any compact Kähler manifold in terms of genus-zero data and residues.