107 research outputs found
The minimal volume orientable hyperbolic 2-cusped 3-manifolds
We prove that the Whitehead link complement and the (-2, 3, 8) pretzel link
complement are the minimal volume orientable hyperbolic 3-manifolds with two
cusps, with volume 3.66... = 4 x Catalan's constant. We use topological
arguments to establish the existence of an essential surface which provides a
lower bound on volume and strong constraints on the manifolds that realize that
lower bound.Comment: 10 pages, 5 figures, incorporated referees comments, includes
hyperref link
Lower bounds on volumes of hyperbolic Haken 3-manifolds
In this paper, we find lower bounds for volumes of hyperbolic 3-manifolds
with various topological conditions. Let V_3 = 1.01494 denote the volume of a
regular ideal simplex in hyperbolic 3-space. As a special case of the main
theorem, if a hyperbolic manifold M contains an acylindrical surface S, then
Vol(M)>= -2 V_3 chi(S). We also show that if beta_1(M)>= 2, then Vol(M)>= 4/5
V_3.Comment: 20 pages, 15 figure
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