论文标题
单颗粒和量子表示的因数
Cosets of monodromies and quantum representations
论文作者
论文摘要
我们使用几何方法来证明任何$ 3 $ -Manifold $ m $，而$ g $是足够大的整数，地图类$ \ mathrm {mathrm {modrm {mod}（σ_{g，1}）$包含一个Abelian Suberian cank $ \ lfloor \ lfloor \ freac \ freac \ freac \ freac {g} g} g} g}的亚洲子群的cast $ M中的开簿分解的伪-Anosov单粒子，我们证明了排名的两个免费coset的$ \ mathrm {modrm {mod}（σ_{g，1}）的结果。$这些结果应用于Andersen，Masbaum和Ueno的构想，大约在表面映射的分类组的量子代表中，对于具有边界和足够大属的表面，我们构造了阿贝尔式的宇宙和自由亚组的映射类群体组成的群体组成的元素，这些组由满足猜想的元素组成。这些元素的映射托架是纤维的3个manifolds，可满足Turaev-Viro不变性体积的弱形式。
We use geometric methods to show that given any $3$-manifold $M$, and $g$ a sufficiently large integer, the mapping class group $\mathrm{Mod}(Σ_{g,1})$ contains a coset of an abelian subgroup of rank $\lfloor \frac{g}{2}\rfloor,$ consisting of pseudo-Anosov monodromies of open-book decompositions in $M.$ We prove a similar result for rank two free cosets of $\mathrm{Mod}(Σ_{g,1}).$ These results have applications to a conjecture of Andersen, Masbaum and Ueno about quantum representations of surface mapping class groups. For surfaces with boundary, and large enough genus, we construct cosets of abelian and free subgroups of their mapping class groups consisting of elements that satisfy the conjecture. The mapping tori of these elements are fibered 3-manifolds that satisfy a weak form of the Turaev-Viro invariants volume conjecture.
