Morava K-理论与球面稳定同伦群

稳定同伦论中一个重要的问题便是球面稳定同伦群的计算，由此问题所发展出来的工具包括Morava K-理论以及谱序列。本项目将考虑与这些工具相关的两个问题：拓扑空间的Morava K-理论的计算以及利用Adams谱序列来计算球面稳定同伦群的非平凡元素。

The computation of the stable homotopy groups of spheres is a very important problem in the stable homotopy theory. Based on this problem people have invented several useful tools included Morava K-theory and spectral sequence. In this project we plan to study two questions related to these tools: computation of the Morava K-theory of a given topological space and the computation of the stable homotopy groups of spheres via the Adams spectral sequence.