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The
level structure in quantum $K$-theory and mock theta
functions
Yongbin Ruan, Ming Zhang and Yaoxiong Wen |
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Geometry & Topology 30 (2026) 835–882
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Abstract |
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This is the first in a sequence of papers to develop the theory of levels in quantum -theory and study its applications. Here, we give an adelic characterization of the range of the -function in quantum -theory with level structure. As an application, we prove a mirror theorem for permutation-equivariant quantum -theory with level structures of toric varieties. In the study of the mirrors of some simple examples, we see the surprising appearance of Ramanujan’s mock theta functions. |
Keywords
quantum $K$-theory, level structure, mock theta function
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Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 14D20, 19E08, 33D15
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References |
Publication
Received: 17 May 2018
Revised: 11 February 2025
Accepted: 4 May 2025
Published: 20 April 2026
Proposed: András I Stipsicz
Seconded: Mark Gross, Arend Bayer
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Authors |
| Yongbin Ruan | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
Institute of Advanced Study for
Mathematics Zhejiang University Hangzhou China |
| Ming Zhang | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| Yaoxiong Wen | |
| School of Mathematics Korea Institute for Advanced Study Seoul South Korea |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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