2018/03/28 by Ігор Протасов, Protasov, Igor, Ksenia Protasova +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1803.10504
openalex publication_date 2018/03/28 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
A coarse group is a group endowed with a coarse structure so that the group multiplication and inversion are coarse mappings. Let (X, E) be a coarse space and let \mathfrakM be a variety of groups different from the variety of singletons. We prove that there is a coarse group F_\mathfrakM (X, E)∈ \mathfrakM such that (X, E) is a subspace of F_\mathfrakM (X, E), X generates F_\mathfrakM (X, E) and every coarse mapping (X, E) \longrightarrow (G, E′) where G∈\mathfrakM, (G, E′) is a coarse group, can be extended to coarse homomorphism F_\mathfrakM (X, E)\longrightarrow (G, E′) . If \mathfrakM is the variety of all groups, the groups F_\mathfrakM (X, E) are asymptotic counterparts of Markov free topological groups over Tikhonov spaces.