dual cohomology class

例句：

1. 1. In the study of differential geometry, dual cohomology plays a crucial role in understanding the topology of manifolds.
   在微分流形的研究中，双共形类在理解拓扑结构方面起着至关重要的作用。
2. 2. The researchers developed a new algorithm to calculate the dual cohomology class of agiven matrix.
   研究人员开发了一种新的算法来计算给定矩阵的双共形类。
3. 3.The dual cohomology class is a key concept in studying the topological properties of manifolds.
   双共形类是研究流形拓扑性质的关键概念。