标题： 关于非定向流形上(2+1)D阿贝尔玻色拓扑系统的维数 显示英文标题

标题： On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds

摘要： 我们提供一个框架，用于在环面中通过$GL(2,\bZ)$的表示来描述具有奇偶对称性的阿贝尔玻色拓扑系统。 然而，仅凭此信息并不能保证我们可以以与拓扑量子场论的粘合公理相容的方式为非定向曲面分配希尔伯特空间。 在这里，我们证明在具有时间反演对称性的阿贝尔玻色拓扑系统的情况下，我们可以为非定向曲面分配具有整数维度的希尔伯特空间。 显示英文摘要

摘要： We give a framework to describe abelian bosonic topological systems with parity symmetry on a torus in terms of the representation of $GL(2,\bZ)$. However, this information alone does not guarantee that we can assign Hilbert spaces to unoriented surfaces in a way compatible with the gluing axiom of topological quantum field theory. Here, we show that we can assign Hilbert spaces with integer dimensions to unoriented surfaces in the case of abelian bosonic topological systems with time-reversal symmetry.