Title: Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle Show Chinese title

Title: 可逆相位对于混合空间对称性和费米子晶体等价原理

Abstract: Freed-Hopkins give a mathematical ansatz for classifying gapped invertible phases of matter with a spatial symmetry in terms of Borel-equivariant generalized homology. We propose a slight generalization of this ansatz to account for cases where the symmetry type mixes nontrivially with the spatial symmetry, such as crystalline phases with spin-1/2 fermions. From this ansatz, we prove as a theorem a "fermionic crystalline equivalence principle," as predicted in the physics literature. Using this and the Adams spectral sequence, we compute classifications of some classes of phases with a point group symmetry; in cases where these phases have been studied by other methods, our results agree with the literature. Show Chinese abstract

Abstract: Freed-Hopkins给出了一个数学假设，用于根据Borel等变广义同调来分类具有空间对称性的间隙可逆物质相。 我们提出对该假设的轻微推广，以考虑对称类型与空间对称性非平凡混合的情况，例如具有自旋-1/2费米子的晶体相。 从这个假设出发，我们作为定理证明了一个“费米子晶体等价原理”，这在物理文献中已有预测。 利用这个原理和Adams谱序列，我们计算了具有点群对称性的某些相类的分类；在这些相已被其他方法研究的情况下，我们的结果与文献一致。