Bordism between Dold and Milnor Manifolds

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

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.

等变Milnor映射

Equivariant Milnor map

将Milnor映射推广到等变情形，证明圆群和二阶循环群的等变酉群上存在该映射，并关联其核与自由共轭的磁等变酉配边群。

典范胞腔流形的特征数及其应用

Characteristic numbers of canonical toric manifolds and their applications

本文计算了典范胞腔流形的陈数、米尔诺数和庞特里亚金数，及其实数对应物的斯蒂夫尔-惠特尼数，探讨了其在单位ary、定向和非定向 bordism 类的组合刻画、单位ary bordism 环生成元的几何代表、典范胞腔流形的边界判定准则以及其浸入欧几里得空间的维数估计。