On toric generators in the unitary and special unitary bordism rings (Q341774)

The authors construct a new family of manifolds generating the unitary bordism ring. Each manifold in the family is toric. It is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. They also construct a family of special unitary quasitoric manifolds which contains polynomial generators of the special unitary bordism ring with 2 inverted in dimensions \(> 8\). Each manifold in the latter family is obtained from an iterated complex projectivisation of a sum of line bundles by amending the complex structure to make the first Chern class vanish.