Motivated by the classical Frobenius problem, we introduce the Frobenius poset on the integers Z, that is, for a sub-semigroup Λ of the non-negative integers (N,+), we define the order by n ≤Λ m if m− n ∈ Λ. When Λ is generated by two relatively prime integers a and b, we show that the order complex of an interval in the Frobenius poset is either contractible or homotopy equivalent to a sphere....
