Title: Non-semisimple WRT at the boundary of Crane-Yetter Show Chinese title

Title: 非半单WRT在Crane-Yetter边界处

Abstract: We prove the slogan, promoted by Walker and Freed-Teleman twenty years ago, that "The Witten-Reshetikhin-Turaev 3-TQFT is a boundary condition for the Crane-Yetter 4-TQFT" and generalize it to the non-semisimple case following ideas of Jordan, Reutter and Walker. To achieve this, we prove that the Crane-Yetter 4-TQFT and its non-semisimple version arXiv:2306.03225 are once-extended TQFTs, using the main result of arXiv:2412.14649. We define a boundary condition, partially defined in the non-semisimple case, for this 4D theory. When the ribbon category used is modular, possibly non-semisimple, we check that the composition of this boundary condition with the values of the 4-TQFT on bounding manifolds reconstructs the Witten-Reshetikhin-Turaev 3-TQFTs and their non-semisimple versions arXiv:1912.02063, in a sense that we make precise. Show Chinese abstract

Abstract: 我们证明了Walker和Freed-Teleman二十年前提出的口号，即“Witten-Reshetikhin-Turaev 3-TQFT是Crane-Yetter 4-TQFT的边界条件”，并根据Jordan、Reutter和Walker的想法将其推广到非半单情况。 为了实现这一点，我们证明了Crane-Yetter 4-TQFT及其非半单版本arXiv:2306.03225是一次扩展的TQFT，使用了arXiv:2412.14649的主要结果。 我们为这个4D理论定义了一个边界条件，在非半单情况下部分定义。 当使用的带饰范畴是模的，可能非半单时，我们验证了该边界条件与4-TQFT在边界流形上的值的组合在某种我们明确的意义下重构了Witten-Reshetikhin-Turaev 3-TQFT及其非半单版本arXiv:1912.02063。