Explicit constructions of bordism of Milnor hypersurface 𝐻_1,𝑛 and ℂ𝑃¹ × ℂ𝑃^𝑛−1

Abstract

In the present paper we construct two new explicit complex bordisms between any two projective bundles over ℂ𝑃¹ of the same complex dimension, including the Milnor hypersurface 𝐻_1,𝑛 and ℂ𝑃¹ × ℂ𝑃^𝑛−1. These constructions reduce the bordism problem to the null-bordism of some projective bundle over ℂ𝑃¹ with the non-standard stably complex structure.