## Annals of Mathematics |

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2-sphere 3-manifold analytic automorphism analytic fibre space assume automorphism Bd F biholomorphic boundary bounded closure cohomology commutative compact completes the proof complex component contains coordinate Corollary corresponding covering cyclic group decomposition defined definition denote diameter less diffeomorphism differentiable manifold disjoint disk element elliptic curves end points equations equivalent exists finite number fixed point fixed-point property follows formula genus geodesoid Haar measure handlebody harmonic function Hence holomorphic function homeomorphism homology homotopy identity imbedding implies induces integral intersection irreducible isomorphism jacobian varieties Let G Lie algebra Lie group linear Math matrix maximal meromorphic function morphism neighborhood non-singular normal notation obtain operator parabolic point proof of Theorem Proposition prove quotient space recursively enumerable resp respect satisfies sequence simple closed curve singular subgroup of G submanifold subspace suppose topology transformation triangulation trivial unique vector