交叉复形纤维化的Exact sequences，映射的同伦分类，群的非交换扩张
Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groups
摘要：
交叉复形的分类空间推广了Eilenberg-MacLane空间的构造。我们展示了如何交叉复合体的纤维化理论允许分析同伦类的地图从一个自由的交叉复杂的这样一个分类空间。这给出了从CW-复形到交叉模的分类空间的映射的同伦分类的结果，并且更一般地，给出了其同伦群在1和n之间的维数为零的交叉复形的同伦分类的结果。其结果类似于群扩张理论中对抽象核的阻塞。
英文摘要：
The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW-complex to the classifying space of a crossed module and also, more generally, of a crossed complex whose homotopy groups vanish in dimensions between 1 and n. The results are analogous to those for the obstruction to an abstract kernel in group extension theory.
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