发表机构
Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo（东京大学宇宙起源研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究玻色子可逆和SPT相，发现高维中首个主要非平凡性是模3现象，指出这与施泰因罗德问题相关，通过托姆的配边理论分析得出迪杰格拉夫 - 维滕相在一般单纯复形和流形上的不同平凡性表现。
AI 中文摘要
玻色子可逆和对称保护拓扑（SPT）相在低维由普通上同调群描述，但高维会出现“超越上同调”相。我们对其进行系统研究，发现首个主要非平凡性是模3现象，而非费米子相的模2现象。我们还指出这是施泰因罗德经典问题的对偶表现，即无流形代表的同调圈的存在问题。托姆发展了配边理论来回答此问题，我们解释了相同分析如何导致在一般单纯复形上非平凡但在流形上平凡的迪杰格拉夫 - 维滕相。
英文摘要
Bosonic invertible and symmetry-protected topological (SPT) phases are well-known to be described by ordinary cohomology groups in low dimensions, but `beyond-cohomology' phases appear in higher dimensions. We make a systematic study of them, and find that the first major non-triviality is a mod-3 phenomenon, and not a mod-2 phenomenon as in the case of fermionic phases. We also point out that this is a dual manifestation of the classic question of Steenrod, namely the issue of the existence of homology cycles without manifold representatives. Thom developed the theory of cobordisms to answer this question, and we explain how the same analysis leads to Dijkgraaf-Witten phases which are nontrivial on general simplicial complexes but become trivial on manifolds.
Comments34 pages + appendix; v2: minor changes in Appendix A and acknowledgments, typos fixed
