EXPLICIT cocycle formulas on finite abelian groups with applications to braided linear Gr-categories and Dijkgraaf–Witten invariants

2017/03/31 by Hua-Lin Huang, Zheyan Wan, Yu Ye
Mathematics · Physics and Astronomy · #Abelian group #Algebraic structures and combinatorial models #Artificial intelligence #Bar (unit) #Computer science #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Resolution (logic) #Torus #math-ph #math.AT #math.MP

paper · pdf · doi:10.1017/prm.2019.15

published as Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2019)

arxiv created 2018/03/22 · openalex created_date 2018/03/29 · openalex publication_date 2019/03/13 · arxiv updated 2019/03/27 · openalex updated_date 2026/08/05

Abstract

Abstract We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution for any given finite abelian group. With a help of the obtained cocycle formulas, we determine all the braided linear Gr-categories and compute the Dijkgraaf–Witten Invariants of the n -torus for all n .

Citations

• Topological interactions in broken gauge theories
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classical and quantum conformal field theory