本文利用任意n维平直空间（平移群流形）到n维球S~n的Kronccker映象，给出平移群的任意高阶同调群上闭链的明显表达式。
An explicit expression for any higher cocycles in translation group is given by means of Kronecker mapping from the n-dimensional flat space ( translation group manifold ) to the n-dimensional sphere .
上闭链