We compute the mapping class group of the manifolds \(\sharp ^g(S^{2k+1}\times S^{2k+1})\) for \(k>0\) in terms of the automorphism group of the middle homology and the group of homotopy \((4k+3)\)-spheres. We furthermore identify its Torelli subgroup, determine the abelianisations, and relate our results to the group of homotopy equivalences of these manifolds.

中文翻译：

---

映射高度连接的$$（4k + 2）$$（4 k + 2）-流形的类组

我们计算映射类组歧管\（\尖锐^克（S ^ {2K + 1} \倍小号^ {2K + 1}）\）为\（K> 0 \）在自同构组的计中间同源性和同构\（（4k + 3）\）-球体组。我们还确定了它的Torelli子组，确定了abelianisation，并将我们的结果与这些流形的同伦等价组联系起来。