Homotopy type of Frobenius complexes

2013/08/13 by Shouta Tounai, Tounai, Shouta
Mathematics · #06A07 #13D40 #55P15 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #msc:06A07 #msc:13D40 #msc:55P15

paper · pdf · doi:10.48550/arxiv.1308.2805

arxiv created 2013/08/13 · arxiv updated 2013/08/15

Abstract

A submonoid A of N^d has a natural order defined by a <= a + b for elements a and b of A. The Frobenius complex is the order complex of an open interval of A with respect to this order. In this paper, the homotopy type of the Frobenius complex of A is determined when A is the submonoid of N generated by two relatively prime integers, or the submonoid of N² generated by three elements of which any two are linearly independent. As an application, the multigraded Poincare series of the quotient algebra K[x, y, z] / (x^p y^q - z^r) over a field K is determined and proved to be rational.

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