AI 中文总结
本文关联统一两类改进可微栈上同调计算的方法：Arias Abad将Bott谱序列推广至李群胚，作者则提出正则真李群胚对应可微栈的上同调模型。
AI 中文摘要
可微栈的上同调可通过Bott-Shulman-Stasheff双复形建模，但在许多例子中计算其上同调仍很困难，改进这一状况需要额外方法，如使用谱序列并寻找该双复形每一列上同调的模型。本文首次尝试关联并统一两类此类方法：其一，Arias Abad通过引入同伦表示将Bott谱序列推广至李群胚；其二，本文作者近期关于正则真李群胚对应的可微栈上同调模型的工作。
英文摘要
The cohomology of a differentiable stack can be modelled by the Bott-Shulman-Stasheff bicomplex. However, computing its cohomology is still difficult in many examples. Improving on this requires additional methods such as using spectral sequences and finding models for the cohomology of each column of the bicomplex. This paper provides a first attempt of relating and unifying two approaches of this form. Firstly, Arias Abad has generalised the Bott spectral sequence to Lie groupoids by introducing representations up to homotopy. The second approach is the recent work on a model for the cohomology of differentiable stacks associated to proper and regular Lie groupoids by this author.
CommentsTo be submitted to the "Special Issue on Interactions of Poisson Geometry, Lie Theory and Symmetry in honor of Rui Loja Fernandes for his 60th birthday" of "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)"
