Calabi Yau Hypersurfaces and SU-Bordism

Abstract

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 ΩSU[12]≅Z[12][yi:i≥2]. We also describe explicit Calabi–Yau representatives for multiplicative generators of the SU-bordism ring in low dimensions.