李群上Orlicz上同调的De Rham定理
De Rham's theorem for Orlicz cohomology in the case of Lie groups
摘要：
在李群的情形下，证明了单纯Orlicz上同调与Orlicz-de Rham上同调的等价性.由于第一个是有界几何的一致可收缩单纯复形的拟等距不变量，我们得到了第二个在可收缩李群的情况下的不变量。我们还定义了Gromov-双曲空间相对于无穷远处边界上一点的Orlicz上同调，对于它也有同样的结果。
英文摘要：
We prove the equivalence between the simplicial Orlicz cohomology and the Orlicz-de Rham cohomology in the case of Lie groups. Since the first one is a quasi-isometry invariant for uniformly contractible simplicial complexes with bounded geometry, we obtain the invariance of the second one in the case of contractible Lie groups. We also define the Orlicz cohomology of a Gromov-hyperbolic space relative to a point on its boundary at infinity, for which the same results are true.
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