On the Existence of Cut Points of Connected Generalized Sierpinski Carpets

I will introduce a characterization of the existence of cut points of connected \linebreak generalized Sierpinski carpets. The criterion is based on examining a finite number of elements in the corresponding Hata graph sequence. Some examples, including connected carpets with \linebreak exactly $m$ cut points, will be presented in addition. This includes some joint works with Xin-Rong Dai, Jun Luo, Huo-Jun Ruan and Yang Wang.