论文标题
扩展的TQFT和代数几何形状
Extended TQFTs and Algebraic Geometry
论文作者
论文摘要
我们研究了一种构建Rozansky的潜在方法 - witten tqft是扩展的$（1+1+1）$ -TQFT。我们构建了一个$ 2 $ - 类别，该类别由方案，束带和捆式形态的复合物组成，并表明在此类别的截断中有价值（1+1）$ - tqfts，其状态空间与Rozansky-witter-Witten TQFT有一致的状态空间。但是，我们还表明，如果这样的TQFT基于减少的Noetherian方案，则不能将其扩展到$（1+1+1）$ -TQFT。
We study a potential method for constructing the Rozansky--Witten TQFT as an extended $(1+1+1)$-TQFT. We construct a $2$-category consisting of schemes, complexes of sheaves and sheaf morphisms and show that there are $(1+1)$-TQFTs valued in the truncation of this category which have state spaces that agree with the Rozansky--Witten TQFT. However, we also show that if such a TQFT is based on a reduced Noetherian scheme, it cannot be extended upwards to a $(1+1+1)$-TQFT.
