论文标题
3D光谱网络和古典Chern-Simons理论
3d spectral networks and classical Chern-Simons theory
论文作者
论文摘要
我们在尺寸$ \ le 3 $的流形上定义了光谱网络的概念。 For a manifold $X$ equipped with a spectral network, we construct equivalences between Chern-Simons invariants of flat ${\mathrm {SL}}(2,{\mathbb C})$-bundles over $X$ and Chern-Simons invariants of flat ${\mathbb C}^\times$-bundles over ramified double covers $\widetilde X$.申请包括有关flat $ {\ mathrm {sl}} flat $ {\ mathbb c}）$ bundles的diogarithmic公式的新观点 - 三角形的3个manifolds上的捆绑包，以及对Chern-simons flat flat $ {slb}的明确描述C}）$ - 三角形表面上的捆绑。我们的构造大量利用了Chern-Simons不变式的局部性，该语言用扩展（可逆的）拓扑领域理论的语言表达。
We define the notion of spectral network on manifolds of dimension $\le 3$. For a manifold $X$ equipped with a spectral network, we construct equivalences between Chern-Simons invariants of flat ${\mathrm {SL}}(2,{\mathbb C})$-bundles over $X$ and Chern-Simons invariants of flat ${\mathbb C}^\times$-bundles over ramified double covers $\widetilde X$. Applications include a new viewpoint on dilogarithmic formulas for Chern-Simons invariants of flat ${\mathrm {SL}}(2,{\mathbb C})$-bundles over triangulated 3-manifolds, and an explicit description of Chern-Simons lines of flat ${\mathrm {SL}}(2,{\mathbb C})$-bundles over triangulated surfaces. Our constructions heavily exploit the locality of Chern-Simons invariants, expressed in the language of extended (invertible) topological field theory.
