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Homotopy type of Frobenius complexes II
release_xixhbop2mjd2dbnp57iauxqrvy
by
Shouta Tounai
Released
as a article
.
2013
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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1311.4620v1
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