solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看2893次
Extending Landau-Ginzburg models to the point. (arXiv:1809.10965v1 [math.QA])
来源于:arXiv
We classify framed and oriented 2-1-0-extended TQFTs with values in the
bicategories of Landau-Ginzburg models, whose objects and 1-morphisms are
isolated singularities and (either $\mathbb{Z}_2$- or $(\mathbb{Z}_2 \times
\mathbb{Q})$-graded) matrix factorisations, respectively. For this we present
the relevant symmetric monoidal structures and find that every object $W \in
\Bbbk[x_1,\dots,x_n]$ determines a framed extended TQFT. We then compute the
Serre automorphisms $S_W$ to show that $W$ determines an oriented extended TQFT
if the associated category of matrix factorisations is $(n-2)$-Calabi-Yau.
The extended TQFTs we construct from $W$ assign the non-separable Jacobi
algebra of $W$ to a circle. This illustrates how non-separable algebras can
appear in 2-1-0-extended TQFTs, and more generally that the question of
extendability depends on the choice of target category. As another application,
we show how the construction of the extended TQFT based on $W=x^{N+1}$ given by
Khovanov a 查看全文>>