2012/03/12 by Danny Stevenson, Stevenson, Danny
Mathematics · #18F20 #18G55 (Primary) #55R35 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1203.2461
openalex publication_date 2012/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we describe a classifying theory for families of simplicial topological groups. If B is a topological space and G is a simplicial topological group, then we can consider the non-abelian cohomology H(B,G) of B with coefficients in G. If G is a topological group, thought of as a constant simplicial group, then the set H(B,G) is the set of isomorphism classes of principal G bundles, or G torsors, on B. For more general simplicial groups G, the set H(B,G) parametrizes the set of equivalence classes of higher G torsors on B. In this paper we consider a more general setting where G is replaced by a simplicial group in the category of spaces over B. The main result of the paper is that under suitable conditions on B and G there is an isomorphism between H(B,G) and the set of isomorphism classes of fiberwise principal bundles on B, with structure group |G| given by the fiberwise geometric realization of G.