For two of these objects X and Y, X is less than Y if X-inverse Y admits a sigma-positive word representation in the Dehornoy (“duh-orn-WAH”) order. A group of these objects can be presented as an ordered set of generators with the relations that non-adjacent generators commute and, for adjacent generators x and y, x y x equals y (-5[1])x y; thus, Artin–Tits (“AHR-tin teets”) groups can be seen as “generalized” groups of these objects. The inner automorphism group of a degree-three group of these objects is isomorphic to the modular group. The Markov (-5[1])theorem gives necessary and sufficient conditions for the equivalence of the closures of these objects, which can be used to represent any (*) knot according (-5[1])to Alexander’s theorem. (-5[3])These objects are typically represented as permutations that follow strings whose crossings (10[1])matter. For 10 points, give these objects named for their representation as interwoven locks of hair. (10[1])■END■ (10[4]0[3])