Artin groups

Artin groups are mathematical structures that generalize braid groups, describing how certain elements (like strands of a rope or wires) can be intertwined. They are defined by generators (basic moves) and relations (rules for how these moves interact), reflecting symmetries and transformations. These groups have applications in topology, algebra, and geometry, helping to understand complex shapes and spaces formed by intertwined objects. Essentially, Artin groups provide a formal way to study and analyze the ways parts can be repeatedly and systematically twisted or rearranged without breaking or tearing, capturing patterns of symmetry and motion in a rigorous framework.