论文标题
拓扑量子场理论的托莱多不变
Toledo invariants of Topological Quantum Field Theories
论文作者
论文摘要
我们证明了fibonAcci量子表示$ρ_{g，n}：\ rm {mod} _ {g，n} \ to \ rm {pu}（p，q）$ for $（g，g，g，n）相应的模量空间的某些压缩$ \ MATHCAL {M} _ {G，N} $的复杂双曲结构。作为推论，在$ \ Mathcal M_ {1,3} $和$ \ Mathcal M_ {1,2} $的相应压缩之间的健忘图是一个紧凑型复杂的复杂的杂交孔径之间的透明性圆锥形图，这是一个高于一个的不同维度的不同维度的答案。 证明包括计算其托莱多不变性：我们将此计算放在更广泛的环境中，用任何Hermitian模块化函数代替了斐波那契表示，并将托莱多不变性扩展到以签名$ p-q $开头的一系列共同体不变性。 我们证明，这些不变的人满足了共同体田地理论的公理，并在第一阶（因此，在任何层面上的$ \ rm {su} _2/\ rm {so} _2/\ rm {so} _2/\ rm {su} _2/\ rm {so} _3 $ -Quantum-Quantum Anceptions中，一阶（因此通常的Toledo noffariants）计算$ r $ -Matrix。
We prove that the Fibonacci quantum representations $ρ_{g,n}:\rm{Mod}_{g,n}\to \rm{PU}(p,q)$ for $(g,n)\in\{(0,4),(0,5),(1,2),(1,3),(2,1)\}$ are holonomy representations of complex hyperbolic structures on some compactifications of the corresponding moduli spaces $\mathcal{M}_{g,n}$. As a corollary, the forgetful map between the corresponding compactifications of $\mathcal M_{1,3}$ and $\mathcal M_{1,2}$ is a surjective holomorphic map between compact complex hyperbolic orbifolds of different dimensions higher than one, giving an answer to a problem raised by Siu. The proof consists in computing their Toledo invariants: we put this computation in a broader context, replacing the Fibonacci representations with any Hermitian modular functor and extending the Toledo invariant to a full series of cohomological invariants beginning with the signature $p-q$. We prove that these invariants satisfy the axioms of a Cohomological Field Theory and compute the $R$-matrix at first order (hence the usual Toledo invariants) in the case of the $\rm{SU}_2/\rm{SO}_3$-quantum representations at any level.
