Homotopy type of Frobenius complexes II release_xixhbop2mjd2dbnp57iauxqrvy

Abstract

A finitely generated additive submonoid Λ of N^d has the partial order defined by λ<λ + μ for λ, μ∈Λ. The Frobenius complex is the order complex of an open interval of Λ. In this paper, we express the homotopy type of the Frobenius complex of Λ[ρ / r] in terms of those of Λ, where Λ[ρ / r] is the additive monoid which is added the r-th part of ρ to Λ. As applications, we determine the homotopy type of the Frobenius complex of some submonoids of N, for example, the submonoid generated by a finite geometric sequence. We also state an application to the multi-graded Poincaré series.
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