Explicit constructions of bordism of Milnor hypersurface H1,n and CP1 × CPn−

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 H1,n and CP1 ×CPn−1. These constructions reduce the bordism problem to the null-bordism of some projective bundle over CP1 with the non-standard stably complex structure. © 2020 The Mathematical Society of Japan