Homotopy Types of Frobenius Complexes

作者：Tounai Shouta^*

来源：Annals of Combinatorics, 2017, 21(2): 317-329.

DOI：10.1007/s00026-017-0353-1

• Frobenius complex
• order complex
• multi-graded Poincare series

Let I > be a submonoid of the additive monoid . There is a natural order on I > defined by for . A Frobenius complex of I > is defined to be the order complex of an open interval of I >. Suppose and let be a reducible element of I >. We construct the additive monoid obtained from I > by adjoining a solution to the equation . We show that any Frobenius complex of is homotopy equivalent to a wedge of iterated suspensions of Frobenius complexes of I >. As a consequence, we derive a formula for the multi-graded Poincar, series associated to . As an application, we determine the homotopy types of the Frobenius complexes of some additive monoids. For example, we show that if I > is generated by a finite geometric sequence, then any Frobenius complex of I > is homotopy equivalent to a wedge of spheres.

• 出版日期2017-6