评估薄平面
Evaluating thin flat surfaces
摘要：
我们认为可识别的评价一个合适的类别的有向二维协边与角之间的有限工会的间隔。我们称这种配边薄平面。评价由两个变量的幂级数给出。可识别的评估对应于二元多项式与两个一元多项式的乘积之比的系列，每个一元多项式对应一个变量。它们也在一个双射与同构类的交换Frobenius代数上的两个发电机与非退化的跟踪固定。后面的n维代数对应于仿射平面上n个点的希尔伯特方案上的对偶重言丛上的点，其中从丛中移除某个因子。一个可识别的评估产生函子从上述的薄平面的配边范畴到有限维向量空间的范畴。这些函子在有趣的情况下可能是非monoidal的。一个可识别的评价，我们也分配一个类似的德利涅范畴和其商的理想可忽略的态射。
英文摘要：
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.
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