homotopy obstruction

例句：

1. 1. In homotopy theory, the concept of a loop is essential for understanding the behavior of certain functions.
   在同构理论中，环的概念对于理解某些函数的行为至关重要。
2. 2.The study of homotopy groups has led to important advances in computer graphics and robotics.
   研究同构群的研究在计算机图形学和机器人学方面取得了重要的进展。
3. 3.The theorem states that two manifolds are homeomorphic if they have the same homotopy type.
   该定理表明，如果两个流形具有相同的同调类型，那么它们是同胚的。