Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Birkhäuser Boston
About this chapter
Cite this chapter
Kapovich, M. (2009). Rips Theory. In: Hyperbolic Manifolds and Discrete Groups. Modern Birkhäuser Classics. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4913-5_12
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4913-5_12
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4912-8
Online ISBN: 978-0-8176-4913-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)