2011/10/14 by Friedrich Wagemann, Wagemann, Friedrich, Christoph Wockel +1
Mathematics · #20J06 (Secondary) #22E41 (Primary) 57T10 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:20J06 #msc:22E41 #msc:57T10
paper · pdf · doi:10.48550/arxiv.1110.3304
LaTeX, 32 pages; v3: minor modifications, Rem. I.8 removed (was incorrect), to appear in Trans. Amer. Math. Soc
openalex publication_date 2011/10/14 · arxiv created 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a unified framework in which the different constructions of cohomology groups for topological and Lie groups can all be treated on equal footings. In particular, we show that the cohomology of "locally continuous" cochains (respectively "locally smooth" in the case of Lie groups) fits into this framework, which provides an easily accessible cocycle model for topological and Lie group cohomology. We illustrate the use of this unified framework and the relation between the different models in various applications. This includes the construction of cohomology classes characterizing the string group and a direct connection to Lie algebra cohomology.