The higher Euler operators, the total inner product and the total homotopy operator constructed for proving the exactness of the horizontal complex are the most important results of this thesis.
为证明水平复形的正合性而构造的高阶欧拉算子、全内积公式和全同伦算子是本文最重要的结果；
The higher Euler operators, the total inner product and the total homotopy operator constructed for proving the exactness of the horizontal complex are the most important results of this thesis.
为证明水平复形的正合性而构造的高阶欧拉算子、全内积公式和全同伦算子是本文最重要的结果；
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