On toric generators in the unitary and special unitary bordism rings

Abstract

We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We 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.

20 pages, minor changes in this version

References in corpus (2)

• Toric Polynomial Generators of Complex Cobordism
• Equivariant bordism of 2-torus manifolds and unitary toric manifolds--a survey

Cited by in corpus (3)

• SU-bordism: structure results and geometric representatives
• Twisted Milnor Hypersurface I
• The explicit geometric constructions of bordism of Milnor hypersurface $H_{1,n}$ and $\mathbb{C}{P}^1\times \mathbb{C}{P}^{n-1}$