تقرير
Toledo invariants of Topological Quantum Field Theories
| العنوان: | Toledo invariants of Topological Quantum Field Theories |
|---|---|
| المؤلفون: | Deroin, Bertrand, Marché, Julien |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Differential Geometry |
| الوصف: | We prove that the Fibonacci quantum representations $\rho_{g,n}:\rm{Mod}_{g,n}\to \rm{PU}(p,q)$ 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. Comment: 57 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.09952 |
| رقم الأكسشن: | edsarx.2207.09952 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |