论文标题
两种De Rham复合物之间的比较
A comparison between two de Rham complexes in diffeology
论文作者
论文摘要
差异学有两个De Rham复合物。最初的是源自源，另一个是由简单差分级代数定义的单数DE RHAM复合物。我们通过使用{\ it因子映射}的{\ it因子映射}来比较了čech--de rham光谱序列中两个复合物的第一个DE RHAM共同体学组。结果，得出的是，非理性的圆环$t_θ$的奇异DE RHAM共同体学代数是原始DE RHAM共同体的张量产物以及由$T_θ$超过$T_θ$产生的原始DE RHAM共同体和外部代数的张量。
There are two de Rham complexes in diffeology. The original one is due to Souriau and the other one is the singular de Rham complex defined by a simplicial differential graded algebra. We compare the first de Rham cohomology groups of the two complexes within the Čech--de Rham spectral sequence by making use of the {\it factor map} which connects the two de Rham complexes. As a consequence, it follows that the singular de Rham cohomology algebra of the irrational torus $T_θ$ is isomorphic to the tensor product of the original de Rham cohomology and the exterior algebra generated by a non-trivial flow bundle over $T_θ$.
