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

2015/09/13 by Alexander Givental, Givental, Alexander · 2 citations
Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1509.03903

openalex publication_date 2015/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first retell in the K-theoretic context the heuristics of\nS¹-equivariant Floer theory on loop spaces which gives rise to D_q-module\nstructures, and in the case of toric manifolds, vector bundles, or\nsuper-bundles to their explicit q-hypergeometric solutions. Then, using the\nfixed point localization technique developed in Parts II--IV, we prove that\nthese q-hypergeometric solutions represent K-theoretic Gromov-Witten\ninvariants.\n

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