A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
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DOI：
10.1016/j.topol.2019.107052
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发表时间：
2018-05
影响因子：
0.6
通讯作者：
Naoya Enomoto;Y. Kuno;T. Satoh
中科院分区：
文献类型：
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作者：
Naoya Enomoto;Y. Kuno;T. Satoh
在前人关于自由群的自同构群的Johnson焦核的一些结果的基础上，利用表示理论的方法引入了曲面映射类群的Johnson焦核中的新类。另一方面，在b[15]中，Kawazumi和第二作者通过对曲面上曲线自交的拓扑考虑引入了另一类类。在本文中，我们证明[15]中发现的类包含在[8]中发现的类的稳定范围内。此外，我们证明了在[8]中获得的m≥1时的抗森田障碍物[1 4 m+ 1]和[6]中检测到的钩型分量[3,1 5]出现在它们的间隙中。
Abstract In [8], the first and the third authors introduced new classes in the Johnson cokernels of the mapping class groups of surfaces by a representation theoretic approach based on some previous results for the Johnson cokernels of the automorphism groups of free groups. On the other hand, in [15], Kawazumi and the second author introduced another type of classes by a topological consideration of self-intersections of curves on a surface. In this paper, we show that the classes found in [15] are contained in the classes found in [8] in a stable range. Furthermore, we prove that the anti-Morita obstructions [1 4 m+ 1] for m≥ 1 obtained in [8] and a hook-type component [3, 1 5] detected in [6] appear in their gap.