2021/01/22 by Irit Huq-Kuruvilla, Huq-Kuruvilla, Irit · 1 citation
Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2101.09305
openalex publication_date 2021/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a twisting theorem for nodal classes in permutation-equivariant quantum K-theory, and combine it with existing theorems of Givental to obtain a twisting result for general characteristic classes of the virtual tangent bundle. Using this result, we develop complex cobordism-valued Gromov-Witten invariants defined via K-theory, and relate those invariants to K-theoretic ones via the quantization of suitable symplectic transformations. The resulting theory is a K-theoretic analogue of the quantum cobordism theory developed by Givental and Coates. Using the universality of cobordism theory, we study the example of "Hirzebruch K-theory", which is the cohomology theory determined by the Hirzebruch χ-y-genus.