格点空间上的垂直泛函复形及其正合性

Vertical Functional Complex on Lattice Space and It's Exactness

在正规格点空间上的垂直形式之间定义等价关系得到泛函形式,并将垂直外微分算子延拓为泛函形式的变分微分,然后由变分微分的幂零性得到垂直泛函复形并构造同伦映射证明它是正合的。

We define an equivalent relation among vertical forms and functional differential on regular lattice space of Lp.And the vertical differential extends to be variation differential which is also nilpotent.Based on the nilpotence of the variational differential,a vertical functional complex can be derived and proved to be exact by constructing homotopy maps.