映射类群和Dupont-Guichardet-Wigner准同态的量子表示的图像
Images of quantum representations of mapping class groups and Dupont-Guichardet-Wigner quasi-homomorphisms
摘要：
证明了量子表示的映射类群的象与高秩格不同构，或者核有大量的正规生成元。进一步证明了映射类群的象至少在小的水平上具有非平凡的2-上同调。为此，我们考虑了一系列准同态的映射类群扩展以前的工作的Barge和Ghys和Gambaudo和Ghys。这些拟同态是伪酉群上的Dupont-Guichardet-Wigner拟同态沿量子表示的拉回。
英文摘要：
We prove that either the images of the mapping class groups by quantum representations are not isomorphic to higher rank lattices or else the kernels have a large number of normal generators. Further we show that the images of the mapping class groups have nontrivial 2-cohomology, at least for small levels. For this purpose we considered a series of quasi-homomorphisms on mapping class groups extending previous work of Barge and Ghys and of Gambaudo and Ghys. These quasi-homomorphisms are pull-backs of the Dupont-Guichardet-Wigner quasi-homomorphisms on pseudo-unitary groups along quantum representations.
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