3-manifold groups have unique asymptotic cones

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.

10 pages

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Divergence and quasimorphisms of right-angled Artin groups
• Finitely presented groups with infinitely many non-homeomorphic asymptotic cones
• Iterated asymptotic cones

Cited by in corpus (2)

• Quasiconvexity in $3$-manifold groups
• Embedding universal covers of graph manifolds in products of trees