Virtually Haken Dehn-filling
1999; Lehigh University; Volume: 52; Issue: 1 Linguagem: Inglês
10.4310/jdg/1214425220
ISSN1945-743X
Autores Tópico(s)Advanced Combinatorial Mathematics
ResumoWe show that "most" Dehn-fillings of a non-fibered, atoroidal, Haken threemanifold with torus boundary are virtually Haken. ResultsSuppose that X is a compact, oriented, three-manifold with boundary a torus T. We will pick a basis of H\ (T) represented by simple loops A,ß such that A = 0 in H\(X; Q).We call A a longitude and /z a meridian.A slope, a, on T is the isotopy class of an essential unoriented simple closed curve.The manifold X(a) is the result of Dehn-filling along the slope a.This means that a solid torus is glued along its boundary to T so that a meridian disc of the solid torus is glued onto a.The manifold X is atoroidal if every Z x Z subgroup of -K\X is conjugate into 7riT.The distance between two slopes a, ß is A (a, ß) which is the absolute value of the algebraic intersection number of the homology classes represented by these slopes.Theorem 1.1.Suppose that X is a compact, connected, oriented, irreducible, atoroidal three-manifold with boundary a torus T. Suppose that S is a compact, connected, oriented, non-separating, incompressible surface properly embedded in X with non-empty boundary.Suppose that S is not a fiber of a fibration of X over the circle.Let g be the genus
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