Ranks of mapping tori via the curve complex

2014/09/05 by Ian Biringer, Biringer, Ian, Juan Souto +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1409.1878

openalex publication_date 2014/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if the monodromy of a 3-manifold M that fibers over the circle has large translation distance in the curve complex, then the rank of the fundamental group of M is 2g+1, where g is the genus of the fiber.

Citations

• Tameness of hyperbolic 3-manifolds
• The structure of a solvmanifold's Heegaard splittings

Related

• Rank and genus of 3-manifolds
• Rank two affine manifolds in genus three
• The monodromy group of a function on a general curve
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• An upper bound on the asymptotic translation lengths on the curve graph and fibered faces