homotopy exact sequence

例句：

1. 1. The study of homotopy theory is crucial for understanding the behavior of complex systems.
   研究同胚理论对于理解复杂系统的行为至关重要。
2. 2. In mathematics, homotopy can be used to study the topology of spaces.
   在数学中，同胚可以用来研究空间的拓扑。
3. 3. The concept of homotopy has applications in various fields, including computer graphics and robotics.
   同胚概念在计算机图形学和机器人学等领域有着广泛的应用。