Divisibility constraints on degrees of factor maps

Trow, Paul

doi:10.1090/S0002-9939-1991-1056686-9

Divisibility constraints on degrees of factor maps
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by Paul Trow

Proc. Amer. Math. Soc. 113 (1991), 755-760

DOI: https://doi.org/10.1090/S0002-9939-1991-1056686-9

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Abstract:

We show that the degree of a finite-to-one factor map $f:{\sum _A} \to {\sum _B}$ between shifts of finite type is constrained by the factors of ${\chi _A}$ and ${\chi _B}$. A special case of these constraints is that if $^*B$, then the degree of $f$ is a unit in $\mathbb {Z}[1/{\det ^*}B]$ (where $^*A$ is the rank of the Jordan form away from 0 of $A$, and ${\det ^*}B$ is the determinant of the Jordan form away from 0 of $B$).

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