拓扑学中的同伦与基本群

Homotopy and Fundamental Group in Topology

摘要: 本文主要研究拓扑空间中同伦的相关性质，进而讨论道路的逆及乘法运算，由此得到基本群，通过证明知基本群为拓扑不变量，最后利用基本群证明二维球面S²不同胚于环面T²。

Abstract: This article mainly studies the relevant properties of homotopy in topological spaces, and then discusses the inverse and multiplication operations of roads, thereby obtaining the fundamental group. By proving that the known fundamental group is a topological invariant, the fundamental group is finally used to prove that the two-dimensional sphere S² is different from the torus T².