Statistics of Random 3-Manifolds occasionally fibering over the circle

2014/01/22 by Igor Rivin, Rivin, Igor · 1 citation
Mathematics · #20F34 #57M50 #57N10 #60B15 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1401.5736

openalex publication_date 2014/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study random elements of subgroups (and cosets) of the mapping class group of a closed hyperbolic surface, in part through the properties of their mapping tori. In particular, we study the distribution of the homology of the mapping torus (with rational, integer, and finite field coefficients, the hyperbolic volume (whenever the manifold is hyperbolic), the dilatation of the monodromy, the injectivity radius, and the bottom eigenvalue of the Laplacian on these mapping tori. We also study mapping tori of punctured surface bundles, and various invariants of their Dehn fillings. We also study corresponding questions in the Dunfield-Thurston model of random Heegard splittings of fixed genus, and give a number of new and improved results in that setting.

Citations

• Semigroups containing proximal linear maps

Cited by

• Compressed data structures for Heegaard splittings

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