Action of M(0,2n) on some kernel spaces coming from SU (2) ‐TQFT
Action of M(0,2n) on some kernel spaces coming from SU (2) ‐TQFT
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M(0,2n) 对来自 SU (2) -TQFT 的某些内核空间的作用
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发表时间：
2016
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通讯作者：
Ramanujan Santharoubane
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作者：
Ramanujan Santharoubane
当n为偶数时，我们研究了由SU（2）-TQFT产生的n-穿孔球的映射类群的表示，当所有穿孔都被相同的整数N <$1着色时。我们证明了Andersen，Masbaum和Ueno的猜想（中所述）对所有N ≠ 2的4-穿孔球面成立。在n × 6个穿刺的情况下，我们证明了伪Anosovs满足同调条件，即它们应该以非平凡的拉伸因子作用在McMullen考虑的n 2重分支覆盖的某些同调特征空间上。主要思想是考虑核空间，它是从skein模到SU（2）-TQFT的自然映射的核。我们的主要定理确定，作为表示映射类组，某些这些核空间的同源本征空间认为麦克马伦。我们关于AMU猜想的结果是通过对量子表象取适当的极限而得到的，在这种极限表象中，这样的核空间可以作为极限表象的子空间出现。
For n an even number, we study representations of the mapping class group of the n ‐punctured sphere arising from SU (2) ‐TQFT when all punctures are colored by the same integer N⩾1 . We prove that the conjecture of Andersen, Masbaum and Ueno (stated in ) holds for the 4‐punctured sphere for all N⩾2 . In the case n⩾6 of punctures, we prove it for the pseudo‐Anosovs satisfying a homological condition, namely they should act with a non‐trivial stretching factor on certain eigenspaces of homology of a n2 ‐fold branched cover considered by McMullen. The main idea is to consider the kernel space which is the kernel of the natural map from the skein module to the SU (2) ‐TQFT. Our main theorem identifies, as representations of mapping class groups, certain of these kernel spaces with homology eigenspaces considered by McMullen. Our results concerning the AMU conjecture are obtained by taking appropriate limits of the quantum representations in which such a kernel space may appear as a subspace of the limit representation.