Four-dimensional graph-manifolds with fundamental groups quasi-isometric to fundamental groups of orthogonal graph-manifolds

2017/11/23 by Smirnov, Aleksandr
#05C05 #20F69(Secondary) #51F99 #55M10 #57N99 (Primary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1711.08678

Abstract

We introduce a topological invariant, it a type of a graph-manifold, which takes natural values. For a 4-dimensional graph-manifold, whose type does not exceed two, it is proved that its universal cover is bi-Lipschitz equivalent to a universal cover of an orthogonal graph-manifold (for any Riemannian metrics on graph-manifolds).

Related

• Quasi-isometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees
• Profinite rigidity of graph manifolds, II: knots and mapping classes
• ℤ_n-manifolds in 4-dimensional graph-manifolds
• Embedding universal covers of graph manifolds in products of trees
• Non-positively curved graph manifolds are virtually fibered over the circle