Free crossed resolutions from simplicial resolutions with given CW-basis

On the second cohomology group of a simplicial group

We give an algebraic proof for the result of Eilenberg and Mac Lane that the second cohomology group of a simplicial group G can be computed as a quotient of a fibre product involving the first two homotopy groups and the first Postnikov invariant of G. Our main tool is the theory of crossed module extensions of groups.

单纯群簇的挠方面

Torsion aspects of varieties of simplicial groups

该研究探讨单纯群的挠理论格，分析其在特定子范畴的限制，证明2-交叉模和群交叉复形范畴的半阿贝尔性并描述其挠理论，还得到新的预挠理论与TTF理论实例。

Freeness conditions for crossed squares and squared complexes

Following Ellis, we investigate the notion of totally free crossed squares and related square complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CW-basis, in terms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely algebraic derivation of a result of Brown and Loday.

公共基复形与部分分解格位

The common basis complex and the partial decomposition poset

本文证明公共基复形与偏分解格位同伦等价，并扩展到更广泛的代数结构。