## Annals of Mathematics |

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### Contents

By Bruce Michael Bennett | 26 |

the inequality for localization and a numerical criterion | 66 |

global aspects of the inequality for localization | 80 |

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a e G algebraic space ambient isotopy analytic assume automorphism boundary bounded branch points canonical system Clifford system coherent sheaf commutes compact orbit completes the proof condition consider contains converges Corollary corresponding defined definition denote diagram diffeomorphism diffeotopy disjoint domain element embedding etale exists extension finite number finite type fixed point foliation follows formal fuchsian group function hence homeomorphism homotopic identity implies induced intersection invariant component irreducible isomorphism kleinian group Lemma Let F Let G manifold Math maximal ideal monoidal transform morphism neighborhood normal subgroup notation number field obtain parabolic polynomial prime ideal proof of Theorem Proposition prove rational Reeb foliation regular regular local ring representation resp respect Riemann Riemann surface ring satisfying sequence sheaf simple closed curve Spec subset subspace Suppose surface theory torus unique vector fields zero