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We introduce the most general to date version of the permutation-equivariant quantum K-theory, and express its total descendant potential in terms of cohomological Gromov-Witten invariants. This is the higher-genus analogue of adelic characterization (Givental–Tonita The Hirzebruch-Riemann–Roch Theorem in True Genus-0 Quantum K-Theory. Noncommutative Geometry, vol. 62, pp. 43–91. MSRI Publication, Berkeley (2014). arXiv:1106.3136), and is based on the application of the Kawasaki-Riemann-Roch formula (Kawasaki, Osaka J. Math. 16(1), 151–159 (1979)) to moduli spaces of stable maps.

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Permutation-Equivariant Quantum K-Theory IX: Quantum Hirzebruch-Riemann-Roch in All Genera

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  • 发表日期：

    2026年

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  • Alexander Givental

摘要

We introduce the most general to date version of the permutation-equivariant quantum K-theory, and express its total descendant potential in terms of cohomological Gromov-Witten invariants. This is the higher-genus analogue of adelic characterization (Givental–Tonita The Hirzebruch-Riemann–Roch Theorem in True Genus-0 Quantum K-Theory. Noncommutative Geometry, vol. 62, pp. 43–91. MSRI Publication, Berkeley (2014). arXiv:1106.3136), and is based on the application of the Kawasaki-Riemann-Roch formula (Kawasaki, Osaka J. Math. 16(1), 151–159 (1979)) to moduli spaces of stable maps.