Low-Dimensional Topology

Low-dimensional topology explores the properties of spaces with small dimensions, particularly one-dimensional (like curves) and two-dimensional (like surfaces) shapes. It studies how these shapes can be twisted, bent, or connected, focusing on their essential characteristics without regard to size or specific measurements. For example, a coffee cup and a doughnut can be considered the same in this context because they can be transformed into each other without cutting or gluing. This field helps us understand complex structures by examining simpler, lower-dimensional examples, and it has applications in various scientific and mathematical disciplines.