Bowen-Franks groups as conjugacy invariants for ${\mathbb{T}}^n$ automorphisms

Abstract

The role of generalized Bowen-Franks groups (BF-groups) as topological conjugacy invariants for ${\mathbb{T}}^n$ automorphisms is studied. Using algebraic number theory, a link is established between equality of BF-groups for different automorphisms ($BF$-equivalence) and an identical position in a finite lattice ($\mathcal{L}$-equivalence). Important cases of equivalence of the two conditions are proved. Finally, a topological interpretation of the classical BF-group $\mathbb{Z}$ in this context is presented.

15 pages