Braids, Hypergeometric Functions, and Lattices

A braided n-path is a set of « paths ct(t) in R 3 (i = 1 , . . . , n) satisfying (1) c,(0 = (*,(>), MO, 0> ' i < * < r2, c ^ ) = P„ C/(r2) e { & , . . ,Ô„}(2) The paths do not intersect. Two braided «-paths are regarded as equivalent if and only if it is possible to deform the one configuration into the other respecting conditions (1) and (2) throughout the deformation; note that one does permit rv r2 to vary so long as rx < r2 is respected. Thus (a) and (b) in Figure 1 represent the same braid. By definition, a braid is an equivalence class of braided «-paths.