完全表示群的渐近维数

以同伦群为群中心的群

Homotopy groups as centers of finitely presented groups

对任意的有限阿贝尔群$A$和$n\geq 3$，构造了一个由显式生成元和显式关系定义的群，使得它的中心是$π_n(ΣK(A,1))$ .

用拓扑观点讨论可表示群的一些性质

Some Properties of Finitely Presented Groups with Topological Viewpoints

本文利用连通多面体和CW-复形的基本群和覆盖空间的一些性质，给出了关于群的一些著名定理的拓扑证明。

复超平面排列的同伦李代数并不一定是直接给出的

The homotopy Lie algebra of a complex hyperplane arrangement is not necessarily finitely presented

我们提出了一个理论，产生几个例子，同伦李代数的一个复杂的超平面安排是不确定的。我们还提出了超平面安排的例子，这个李代数的包络代数有一个无理希尔伯特级数。这回答了Denham和Suciu的两个问题。

A finitely presented ${E}_{\infty}$-prop I: algebraic context

We introduce a finitely presented prop $\mathcal{S} = \{\mathcal{S}(n,m)\}$ in the category of differential graded modules whose associated operad $U(\mathcal{S})=\{\mathcal{S}(1,m)\}$ is a model for the $E_\infty$-operad. This finite presentation allows us to describe a natural $E_\infty$-coalgebra structure on the chains of any simplicial set in terms of only three maps: the Alexander-Whitney diagonal, the augmentation map, and an algebraic version of the join of simplices. The first appendix connects our construction to the Surjection operad of McClure-Smith and Berger-Fresse. The second es…