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arXiv · 2101.09305

Multiplicative Quantum Cobordism Theory

Irit Huq-Kuruvilla
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Abstract

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 $\chi_{-y}$-genus.

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Irit Huq-Kuruvilla. 2021-01-22. Multiplicative Quantum Cobordism Theory. https://arxiv.org/abs/2101.09305

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