论文标题
张量平坦链和应用的变形定理（补充“张量可重新配置的G-flat链”）
A deformation theorem for tensor flat chains and applications (complement to ''Tensor rectifiable G-flat chains'')
论文作者
论文摘要
在本说明中，我们将White的G-Flat链的变形定理扩展到G-Flat张量链的设置。作为推论，我们可以获得正常张量链的组识别一些正常链的亚组。此外，相应的自然组同构相对于基于坐标切片质量的规范是等值的。 k链的坐标切片质量是其0个沿沿编成k的所有坐标平面的质量的积分。这个数量等同于通常的质量的事实并不简单。为了证明这一点，我们使用定理的变形定理和针对所有链（不仅有限质量）定义的限制性操作员的部分扩展。相反，除了在某些限制或退化情况下，张量链和有限的质量张链链的整个组并不能自然地与链条亚组相同。
In this note we extend White's deformation theorem for G-flat chains to the setting of G-flat tensor chains. As a corollary we obtain that the groups of normal tensor chains identify with some subgroups of normal chains. Moreover the corresponding natural group isomorphisms are isometric with respect to norms based on the coordinate slicing mass. The coordinate slicing mass of a k-chain is the integral of the mass of its 0-slices along all coordinate-planes of codimension k. The fact that this quantity is equivalent to the usual mass is not straightforward. To prove it, we use the deformation theorem and a partial extension of the restriction operator defined for all chains (not only of finite mass). On the contrary, except in some limit or degenerate cases, the whole groups of tensor chains and of finite mass tensor chains do not identify naturally with subgroups of chains.
