We completely describe the algebraic part of the rational cohomology of the Torelli groups of the manifolds$\#^{g}S^{n}\times S^{n}$relative to a disc in a stable range, for$2n\geqslant 6$. Our calculation is also valid for$2n=2$assuming that the rational cohomology groups of these Torelli groups are finite-dimensional in a stable range.

中文翻译：

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关于 TORELLI 群的上同调

我们完整地描述了流形的 Torelli 群的有理上同调的代数部分$\#^{g}S^{n}\次 S^{n}$相对于稳定范围内的盘，对于$2n\geqslant 6$. 我们的计算也适用于$2n=2$假设这些 Torelli 群的有理上同调群在稳定范围内是有限维的。