An algorithm to detect laminar 3-manifolds
We show that there are algorithms to determine if a 3-manifold contains an essential lamination or a Reebless foliation.
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arXiv subjects
Ian Agol
Publications and source records attributed to Ian Agol.
Volume change under drilling
Given a hyperbolic 3-manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable hyperbolic 3-manifold has volume >.32 .
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Small 3-manifolds of large genus
We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary parallel. This implies the existence of irreducible non-Haken 3-manifolds of arbitrarily high Heegaard genus.
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The Bianchi groups are subgroup separable on geometrically finite subgroups
We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for manifolds commensurable with these groups, immersed incompressible surfaces lift to embeddings in a finite sheeted covering.
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Bounds on exceptional Dehn filling
We show that for a hyperbolic knot complement, all but at most 12 Dehn fillings are irreducible with infinite word-hyperbolic fundamental group.
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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.
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