3-manifold groups have unique asymptotic cones

2011/09/21 by Alessandro Sisto, Sisto, Alessandro · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1109.4674

openalex publication_date 2011/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the (minimal) tree-graded structure of asymptotic cones of non-geometric graph manifold groups, and as a consequence we show that all said asymptotic cones are bilipschitz equivalent. Combining this with geometrization and other known results we obtain that all asymptotic cones of a given 3-manifold group are bilipschitz equivalent.

Citations

• Ricci flow with surgery on three-manifolds
• Divergence and quasimorphisms of right-angled Artin groups

Cited by

• Quasiconvexity in 3-manifold groups

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• Separable and tree-like asymptotic cones of groups
• Tree-graded spaces and asymptotic cones of groups
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