A spectral sequence for the K-theory of tiling spaces
A spectral sequence for the K-theory of tiling spaces
复制标题
平铺空间 K 理论的谱序列
DOI：
10.1017/s0143385708000539
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发表时间：
2007
影响因子：
0.9
通讯作者：
J. Bellissard
中科院分区：
文献类型：
--
作者：
J. Savinien;J. Bellissard
抽象是具有有限的局部复杂性的一个大安排和重复的平铺。语音精确的序列。纤维。
Abstract Let ? be an aperiodic and repetitive tiling of ℝd with finite local complexity. We present a spectral sequence that converges to the K-theory of ? with page-2 given by a new cohomology that will be called PV in reference to the Pimsner–Voiculescu exact sequence. It is a generalization of the Serre spectral sequence. The PV cohomology of ? generalizes the cohomology of the base space of a fibration with local coefficients in the K-theory of its fiber. We prove that it is isomorphic to the Čech cohomology of the hull of ? (a compactification of the family of its translates).