Alexander's Theorem

Alexander's Theorem states that every knot or link in three-dimensional space can be represented as a closed braid. Essentially, it means that any tangled loop or interconnected loops can be rearranged into a form where they look like strands of hair woven into a braid, with the ends joined smoothly. This is significant because it allows mathematicians to study complex knots by analyzing their equivalent braid forms, simplifying the understanding of their structures and properties. The theorem provides a foundational link between knots and braids, facilitating advancements in topology and knot theory.