Word equations in a band of paths
James D. B. Nelson, Mohan S. Putcha · Pacific Journal of Mathematics · 1979
In this paper we introduce a multiplication of paths which yields an idempotent semigroup.We study the properties of this band and solve all word equations in this band.Multiplying paths in a topological space by concatenation is a classical idea in algebraic topology.However, in R n , identifying up to homotopy trivializes all paths.There are many ways of obtaining associativity with less identification.Looking only at the images of the paths in R n , yields an inverse semigroup (cf.[6]).Lesser identifications lead to semigroups which locally resemble free semigroups [4,5].