风车镶嵌的PV上同调、共不变量的整群和空位标记
PV cohomology of pinwheel tilings, their integer group of coinvariants and gap-labelling
摘要：
在本文中，我们首先提醒我们如何可以看到“壳”的风车平铺作为一个逆极限的单纯复形（安德森和普特南），然后我们适应PV上同调引入Bellissard和Savinien的一份文件中定义它的风车平铺。然后我们证明了这个上同调同构于由$S^1$的包的商的整数Čech上同调，这让我们证明了包的顶部整数Čech上同调实际上是包的某些断面上的共不变量的整数群。最后，我们证明了风车镶嵌的间隙标记，并通过一个明确的计算来结束这篇文章，表明$μ^t \big(C(Ξ,\ZZ) \big) = \dfrac{1}{264} \ZZ [\dfrac{1}{5}]$。
英文摘要：
In this paper, we first remind how we can see the "hull" of the pinwheel tiling as an inverse limit of simplicial complexes (Anderson and Putnam) and we then adapt the PV cohomology introduced in a paper of Bellissard and Savinien to define it for pinwheel tilings. We then prove that this cohomology is isomorphic to the integer Čech cohomology of the quotient of the hull by $S^1$ which let us prove that the top integer Čech cohomology of the hull is in fact the integer group of coinvariants on some transversal of the hull. The gap-labelling for pinwheel tilings is then proved and we end this article by an explicit computation of this gap-labelling, showing that $μ^t \big(C(Ξ,\ZZ) \big) = \dfrac{1}{264} \ZZ [\dfrac{1}{5}]$.
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