Topological Degree of Shift Spaces on Monoids

Abstract

This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are determined by a matrix $A$, the coefficients of the characteristic polynomial of $A$ are revealed as the number of children of the graph. After introducing an algorithm for the computation of the degree, the degree spectrum, which is finite, relates to a collection of matrices in which the sum of each row of every matrix is bounded by the number of children of the graph. Furthermore, the algorithm extends to $G$ of finite free-followers.