利用经典Adams谱序列和Adams-Novikov谱序列研究球面和其他一些谱的稳定同伦群是代数拓扑中的一个重要研究方向。Motivic 稳定同伦源自于代数几何，通过Motivic Adams谱序列建立了经典Adams谱序列和代数Novikov谱序列的直接联系。使得我们有更多的办法计算Adams谱序列的E2项和高价Adams微分。Rothenberg-Steenrod谱序列是利用紧Lie群的同调和全空间的同调研究轨道空间的同调、上同调的一种方法。已被提出许多年了，但至今很少利用这个谱序列具体计算。在本项目中我们将借鉴Motivic Adams谱序列利用各种谱序列计算Adams-Novikov谱序列的E2项和高价Adams微分并由此计算球面、MO<8>、T(n)等谱的稳定同伦群。利用Rothenberg-Steenrod谱序列研究环面拓扑中环面对moment-angle流形的作用及提升问题

To determine the stable homotopy groups of spectra by the classical Adams spectral sequence and by the Adams-Novikov spectral sequence is one of the most important problems in algebraic topology. Motivic stable homotopy theory comes from algebraic geometry. More relations between the classical Adams spectral sequence and algebraic Novikov spectral sequence can be seen from the Motivic Adams spectral sequence. By which we have more methods to determine the E2 term and higher Adams differentials. Rothenberg-Steenrod spectral sequence is a method to determine the homology, cohomology of the orbid space from that of the Lie group and of the total space. It was introduced many years ago, but very few people use it. In this project we will use Motivic Adams spectral sequence and many other spectral sequences to compute the E2-term of the Adams-Novikov spectral sequence and higher Adams differentials. By which we will compute the stable homotopy groups of sphere, MO<8>, T(n) etc. We also study the tours action on real and complex moment-angle manifolds and lifting problem in toric topology by the Rothenberg-Steenrod spectral sequence.