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arXiv · 1308.2805

Homotopy type of Frobenius complexes

Shouta Tounai
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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 N^2 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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Shouta Tounai. 2013-08-13. Homotopy type of Frobenius complexes. https://arxiv.org/abs/1308.2805

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