Homotopy type of Frobenius complexes II

2013/11/19 by Shouta Tounai, Tounai, Shouta
Mathematics · #06A07 #13D40 #55E15 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #msc:06A07 #msc:13D40 #msc:55E15

paper · pdf · doi:10.48550/arxiv.1311.4620

arxiv created 2013/11/19 · arxiv updated 2013/11/20

Abstract

A finitely generated additive submonoid Λ of \mathbb 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 \mathbb 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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