Geodesic
$SU$-bordism: structure results and geometric representatives
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 3, pp. 461-524

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The first part of this survey gives a modernised exposition of the structure of the special unitary bordism ring, by combining the classical geometric methods of Conner–Floyd, Wall, and Stong with the Adams–Novikov spectral sequence and formal group law techniques that emerged after the fundamental 1967 paper of Novikov. In the second part toric topology is used to describe geometric representatives in $SU$-bordism classes, including toric, quasi-toric, and Calabi–Yau manifolds. Bibliography: 56 titles.
Keywords: special unitary bordism, $SU$-manifolds, Chern classes, toric varieties, quasi-toric manifolds, Calabi–Yau manifolds. 
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I. Yu. Limonchenko; T. E. Panov; G. S. Chernykh. $SU$-bordism: structure results and geometric representatives. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 74 (2019) no. 3, pp. 461-524. http://geodesic.mathdoc.fr/item/RM_2019_74_3_a3/