论文标题
代数作业的切线同谋的光谱序列
A spectral sequence for tangent cohomology of algebraic operads
论文作者
论文摘要
经营切线的共同体学概括了哈里森共同学的现有理论，雪佛兰 - 埃伦贝格的同谋和Hochschild共同体。这些通常是不乏味的。我们通过产生光谱序列来补充现有的计算技术，该频谱序列将固定代数的运营切线共同体收敛。我们的主要技术工具是由代数的联合振动塔引起的过滤，它们在拓扑空间中扮演着相同的角色连接图和骨骼过滤的作用。 作为一种应用，我们考虑了拓扑空间上的理性亚当斯 - 希尔顿的结构，在该空间中，我们的光谱序列产生了对塞雷光谱序列的看似新的，完全代数的描述，我们也表明，这是乘法性的，并收敛到chas- sullivan循环产品。最后，我们考虑了纤维化$ p $的相对sullivan--de rham模型，我们的频谱序列会收敛于$ p $的自纤维同质均值等效范围的身份分量的理性同拷贝组。
Operadic tangent cohomology generalizes the existing theories of Harrison cohomology, Chevalley--Eilenberg cohomology and Hochschild cohomology. These are usually non-trivial to compute. We complement the existing computational techniques by producing a spectral sequence that converges to the operadic tangent cohomology of a fixed algebra. Our main technical tool is that of filtrations arising from towers of cofibrations of algebras, which play the same role cell attaching maps and skeletal filtrations do for topological spaces. As an application, we consider the rational Adams--Hilton construction on topological spaces, where our spectral sequence gives rise to a seemingly new and completely algebraic description of the Serre spectral sequence, which we also show is multiplicative and converges to the Chas--Sullivan loop product. Finally, we consider relative Sullivan--de Rham models of a fibration $p$, where our spectral sequence converges to the rational homotopy groups of the identity component of the space of self-fiber homotopy equivalences of $p$.
