多面体积上的环与对角排列
Loops on polyhedral products and diagonal arrangements
摘要：
本文建立了由一个单纯复形K（所谓的多面体积）定义的广义楔形的闭路空间同调与K相关联的某些对角排列的同调之间的联系。我们说明了这些结果，通过发现这些循环同调代数的某些K推广Panov-Ray，Papadima-Suciu，Lemaire的结果的介绍。最后，我们表明，在函子被施加到悬浮液的情况下，这种同调分裂来自稳定的同伦分裂的闭路空间。
英文摘要：
In this paper we establish a connection between the loop space homology of the generalization of wedge defined by a simplicial complex K (so called polyhedral product) and the homology of certain diagonal arrangements associated with K. We illustrate these results by finding the presentations of those loop homology algebras for certain K generalizing results of Panov-Ray, Papadima-Suciu, Lemaire. Finally, we show that in the case when the functor is applied to suspensions, this homology splitting comes from the stable homotopy splitting of the loop spaces.
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