Braid Groups

Braid groups are mathematical structures that describe how multiple strands or strings can be intertwined without cutting or tearing them. Imagine several threads hanging parallel; braiding them involves crossing strands over one another in various ways. Each arrangement corresponds to a unique "braid." These braids can be combined by attaching one after another, forming a group with rules about how braids can be manipulated. Braid groups help understand complex patterns in mathematical fields like topology, algebra, and cryptography, providing a formal way to study the possible ways strands can be intertwined while respecting their connections.