Chromatic Homotopy Theory
《Chromatic Homotopy Theory》 · 第 95–96 页 · Section 3.4.8，Figure 3.16 的中间基本域及 Klein bottle 的群生成元
Flat manifolds more complicated than tori can be constructed by considering also non-translational isometries of \(\mathbb R^n\), which exist for \(n\ge3\) and also for \(n=2\) in the non-orientable setting. For instance, in dimension two we find the Klein bottle by taking \(\Gamma\) as the group generated by the isometries: \(\tau:(x,y)\mapsto(x+1,y)\), \(\eta:(x,y)\mapsto(1-x,y+1)\). A fundamental domain for the Klein bottle is shown in Figure 3.16-(centre).