Transactions of the american mathematical society vol:355 issue:3 pages:1067-1077
In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient E\L, where L is a connected and simply connected nilpotent Lie group and E is a torsion-free uniform discrete subgroup of LxC, with C a compact subgroup of Aut( L). We show that if the Lie algebra of L is homogeneous (i.e., graded and generated by elements of degree 1), then the corresponding infra-nilmanifolds admit an expanding map. This is a generalization of the result of H. Lee and K. B. Lee, who treated the 2-step nilpotent case.