论文标题
部分可观测时空混沌系统的无模型预测
Motivic Pontryagin classes and hyperbolic orientations
论文作者
论文摘要
我们介绍了动机环光谱的双曲线取向的概念，该频谱概括了各种现有方向的概念（由GL，SLC，SL，SL，SP）组成。我们表明，ETA - 周期性环光谱的双曲方向对应于Pontryagin类的理论，这与任意环光谱的GL-取向对应于Chern类别的理论一样。我们证明，通过计算Etale分类的空间BGLN的共同体，ETA - 周期性的夸张的共同体学理论不接受进一步的矢量束特征类别。最后，我们构建了通用的夸张的ETA - 周期性交换动机环光谱，这是Voevodsky的Coobordism Spectrum MGL的类似物。
We introduce the notion of hyperbolic orientation of a motivic ring spectrum, which generalises the various existing notions of orientation (by the groups GL, SLc, SL, Sp). We show that hyperbolic orientations of eta-periodic ring spectra correspond to theories of Pontryagin classes, much in the same way that GL-orientations of arbitrary ring spectra correspond to theories of Chern classes. We prove that eta-periodic hyperbolically oriented cohomology theories do not admit further characteristic classes for vector bundles, by computing the cohomology of the etale classifying space BGLn. Finally we construct the universal hyperbolically oriented eta-periodic commutative motivic ring spectrum, an analog of Voevodsky's cobordism spectrum MGL.
