Calabi Yau Hypersurfaces and SU-Bordism

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V. V. Batyrev constructed a family of Calabi–Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi–Yau manifolds whose SU-bordism classes generate the special unitary bordism ring $${\Omega ^{SU}}[\frac{1}{2}] \cong Z[\frac{1}{2}][{y_i}:i \geqslant 2]$$ . We also describe explicit Calabi–Yau representatives for multiplicative generators of the SU-bordism ring in low dimensions.