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Permutation-equivariant quantum K-theory V. Toric $q$-hypergeometric functions

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arxiv 1509.03903 v1 pith:F62RMZUF submitted 2015-09-13 math.AG

Alexander Givental This is my paper · ORCID
classification math.AG
keywords hypergeometrick-theoreticsolutionstoricbundlescasecontextdeveloped
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abstract

We first retell in the K-theoretic context the heuristics of $S^1$-equivariant Floer theory on loop spaces which gives rise to $D_q$-module structures, and in the case of toric manifolds, vector bundles, or super-bundles to their explicit $q$-hypergeometric solutions. Then, using the fixed point localization technique developed in Parts II--IV, we prove that these $q$-hypergeometric solutions represent K-theoretic Gromov-Witten invariants.

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  1. Towards small quantum Chern character

    math.AG 2025-07 conditional novelty 7.0 of 10

    A quantum Chern character ring homomorphism is constructed for projective spaces and incidence varieties, and a new presentation of small quantum K-theory of Milnor hypersurfaces is proved.

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