2014/10/03 by Shouta Tounai, Tounai, Shouta
Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #math.CO
paper · pdf · doi:10.48550/arxiv.1410.1388
arxiv created 2014/10/03 · arxiv updated 2014/10/07
An affine monoid is an additive monoid which is cancellative, pointed and finitely generated. An affine monoid Λ has the partial order defined by λ≤ λ+ μ. The Frobenius complex is the order complex of an open interval of Λ with respect to this partial order. The reduced homology of the Frobenius complex is related to the torsion group of the monoid algebra K[Λ]. In this paper, we pay attention to homotopy types of Frobenius complexes, and we express the homotopy types of the Frobenius complexes of Λ in terms of those of Λ1 and Λ2 when Λ is an affine monoid obtained by gluing two affine monoids Λ1 and Λ2 with one relation. We also state an application to the Poincaré series of the torsion group of the monoid algebra.