Statistics of Random 3-Manifolds occasionally fibering over the circle

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.

36 pages, many figures, v3 is basically a new paper (but includes the old paper as a proper subset). V4 includes results on mapping tori of cusped surfaces (including their Dehn fillings)

References in corpus (1)

• Generic Phenomena in Groups -- Some Answers and Many Questions

Cited by in corpus (5)

• Volumes of random 3-manifolds
• The Smallest Positive Eigenvalue Of Fibered Hyperbolic 3-Manifolds
• Morse theory and Lescop's equivariant propagator for 3-manifolds with $b_1=1$ fibered over $S^1$
• Experiments with the Census
• The twist-cofinite topology on the mapping class group of a surface