Consider a pared 3-manifold (M, P) with incompressible boundary \(\partial_0 M\); let W ⊂ M be the window of (M, P) and let G= π1 (M). We call an action G↷ (M) on a metric tree relatively elliptic (with respect to P) if the fundamental group of each component of the parabolic locus P has a global fixed point in T. The following theorem is crucial for the proof of the Hyperbolization Theorem as presented in this book.
KeywordsFundamental Group Vertex Group Measured Foliation Band Complex Transversal Measure
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