Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle

2023/08/01 by Cheetham-West, Tamunonye · 1 citation
#57K20 (Secondary) #57K32 (Primary) 20E18 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2308.00266

Abstract

We show that hyperbolic four-punctured S²-bundles over S¹ are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a fiber is detected by the profinite completion of the fundamental group of a fibered hyperbolic 3-manifold.

Cited by

• Toward the profinite rigidity of hyperbolic 3-manifolds

Related

• Absolute profinite rigidity of some closed fibered hyperbolic 3-manifolds
• Toward the profinite rigidity of hyperbolic 3-manifolds
• Profinite rigidity, fibering, and the figure-eight knot
• Rigidity results for certain 3-dimensional singular spaces and their fundamental groups
• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle