Abstract
We prove the genus-one restriction of the all-genus Landau–Ginzburg/Calabi–Yau conjecture of Chiodo and Ruan, stated in terms of the geometric quantization of an explicit symplectomorphism determined by genus-zero invariants. This gives the first evidence supporting the higher-genus Landau–Ginzburg/Calabi–Yau correspondence for the quintic $3$ -fold, and exhibits the first instance of the ‘genus zero controls higher genus’ principle, in the sense of Givental’s quantization formalism, for non-semisimple cohomological field theories.
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