AI 中文总结
本文针对球形有限张量范畴C，结合相关文献的三维流形不变量与色映射，通过通用构造定义了一类取值于向量空间的非半单开-闭三维拓扑场论。
AI 中文摘要
给定一个不一定是半单的球形有限张量范畴C，以及其投射理想上的双侧修正迹，我们定义了一个取值于向量空间的开-闭三维拓扑场论。配边范畴的态射是带角的三维配边，其边界被划分为粘合边界（由源和靶曲面参数化）与非参数化的自由边界；自由边界上配备了满足可容许性条件的嵌入C着色图。我们的构造基于两个来源：一是arXiv:1809.07991的多把手体不变量，二是arXiv:2302.04509的色映射，从这两者出发得到新的三维流形不变量，再通过通用构造得到该开-闭拓扑场论。
英文摘要
Given a spherical finite tensor category C, not necessarily semisimple, and a two-sided modified trace on its projective ideal, we define an open-closed three-dimensional topological field theory with values in vector spaces. The bordism category has as morphisms three-dimensional bordisms with corners, whose boundary is partitioned into the gluing boundary, parametrised by source and target surface, and the unparametrised free boundary. The free boundary is equipped with an embedded C-coloured graph satisfying an admissibility condition. Our construction starts from a new three-manifold invariant based on the multi-handlebody invariant of [arXiv:1809.07991] and the chromatic maps of [arXiv:2302.04509]. The open-closed topological field theory is then obtained via the universal construction.
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