The explicit geometric constructions of bordism of Milnor hypersurface $H_{1,n}$ and $\mathbb{C}{P}^1\times \mathbb{C}{P}^{n-1}$

Abstract

In the present paper we construct two new explicit complex bordisms between any two projective bundles over $\mathbb{C}{P}^1$ of the same complex dimension, including the Milnor hypersurface $H_{1,n}$ and $\mathbb{C}{P}^1\times \mathbb{C}{P}^{n-1}$. These constructions reduce the bordism problem to the null-bordism of some projective bundle over $\mathbb{C}{P}^1$ with the non-standard stably complex structure.

Minor typos corrected, added outline of main result. 10 pages, 1 figure