m;">k</span></span></span></span>-fold ones.
We introduce the theory of letter-braiding invariants—these are “polynomial” functions on words, inspired by the homotopy theory of loop-spaces and Koszul duality, and carrying deep geometric content.
They extend the influential Magnus expansion of free groups, which already had countless applications in low dimensional topology, into a functor defined on arbitrary groups.
As a consequence we get new combinatorial formulas for braid and link invariants, and