The maximal number of exceptional Dehn surgeries

摘要: Thurston’s hyperbolic Dehn surgery theorem is one of the most important results in 3-manifold theory, and it has stimulated an enormous amount research. If M a compact orientable with boundary single torus, then asserts that, for all but finitely many slopes s on ∂M , manifold M(s) obtained by filling along also admits structure. The where not are known as exceptional. A major open question been: what maximal number exceptional such M? When exterior figure-eight knot, 10, this was conjectured Gordon [19] to be upper bound that holds . In paper, we prove conjecture.