论文标题
评估薄扁平表面
Evaluating thin flat surfaces
论文作者
论文摘要
我们考虑对适当类别的定向二维协调的可识别评估，并在有限的间隔工会之间拐角。我们称这种恢复性薄扁平表面。评估由两个变量的功率序列给出。可识别的评估对应于两个单变量多项式的乘积，是两个变量多项式的序列，每个变量一个。他们还在两种发电机上的同构frobenius代数的同构类别中，其固定痕迹。尺寸n的后一个代数对应于仿射平面上N点的希尔伯特方案上的双重言式束上的点，从束从束中取出了一定的除数。可识别的评估从上面的薄扁平表面上的上述共同体类别引起了函子，到有限维矢量空间的类别。在有趣的情况下，这些函子可能是非旋转的。为了进行可识别的评估，我们还通过可忽略不计的形态的理想来分配磨难类别及其商的类似物。
We consider recognizable evaluations for a suitable category of oriented two-dimensional cobordisms with corners between finite unions of intervals. We call such cobordisms thin flat surfaces. An evaluation is given by a power series in two variables. Recognizable evaluations correspond to series that are ratios of a two-variable polynomial by the product of two one-variable polynomials, one for each variable. They are also in a bijection with isomorphism classes of commutative Frobenius algebras on two generators with a nondegenerate trace fixed. The latter algebras of dimension n correspond to points on the dual tautological bundle on the Hilbert scheme of n points on the affine plane, with a certain divisor removed from the bundle. A recognizable evaluation gives rise to a functor from the above cobordism category of thin flat surfaces to the category of finite-dimensional vector spaces. These functors may be non-monoidal in interesting cases. To a recognizable evaluation we also assign an analogue of the Deligne category and of its quotient by the ideal of negligible morphisms.
