谱三元组与分形几何
算子代数
2011-09-22 v2 K理论与同调
摘要
对于谢尔宾斯基地毯的每个K-同调元，我们构造一个能生成该元的谱三元组。我们证明，若要该谱三元组能恢复地毯的几何性质，则对K-同调元的选择必须施加某些限制。对于K-同调群的一个大子群，我们证明所构造的谱三元组能恢复地毯上的度量、维数和Hausdorff测度。
引用
@article{arxiv.1002.3081,
title = {Spectral triples and the geometry of fractals},
author = {Erik Christensen and Cristina Ivan and Elmar Schrohe},
journal= {arXiv preprint arXiv:1002.3081},
year = {2011}
}
备注
29 pages, 9 figures, The title in the first version was: "On the choice of a spectral triple". The title and parts of the manuscript have been changed in accordance with suggetions made by the referee. The article will appear in Journal of noncommutative geometry