Ornate necklaces and the homology of the genus one mapping class group
Ornate necklaces and the homology of the genus one mapping class group
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华丽项链与属一映射类群的同源性
DOI：
10.1112/blms/bdm076
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发表时间：
2006
影响因子：
0.9
通讯作者：
James F. Conant
中科院分区：
文献类型：
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作者：
James F. Conant
根据Kontsevich的开创性工作，一个曲面的映射类群的不稳定同调可以通过某个李代数的同调来计算。在最近的一篇论文中，S.Morita分析了这个李代数的简单化，从而在映射类群的同调中构造了一系列不稳定类的候选者。本文证明了这些圈都是非平凡的，表示满足k-⩾-1-mod-4的所有k-≡-5在HK(M1kq)Sk中的同调类.这里M1k是一个具有k个穿孔的亏格的映射类群.
According to seminal work of Kontsevich, the unstable homology of the mapping class group of a surface can be computed via the homology of a certain Lie algebra. In a recent paper, S. Morita analyzed the abelianization of this Lie algebra, thereby constructing a series of candidates for unstable classes in the homology of the mapping class group. In the current paper, we show that these cycles are all nontrivial, representing homology classes in Hk(M1kQ)Sk for all k ⩾ 5 satisfying k ≡ 1 mod 4. Here M1k is the mapping class group of a genus one surface with k punctures.