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Geometrisation of 3-Manifolds

Laurent Bessières, Gérard Besson, Michel Boileau, Sylvain Maillot, and Joan Porti
Publisher: 
European Mathematical Society
Publication Date: 
2010
Number of Pages: 
237
Format: 
Hardcover
Series: 
Tracts in Mathematics 13
Price: 
64.00
ISBN: 
9783037190821
Category: 
Monograph
We do not plan to review this book.
  • The Geometrisation conjecture

Part I. Ricci flow with bubbling-off: definitions and statements

  • Basic definitions
  • Piecing together necks and caps
  • $\kappa$-noncollapsing, canonical geometry and pinching
  • Ricci flow with $(r, \delta, \kappa)$-bubbling-off

Part II. Ricci flow with bubbling-off: existence

  • Choosing cutoff parameters
  • Metric surgery and the proof of Proposition A
  • Persistence
  • Canonical neighbourhoods and the proof of Proposition B
  • $\kappa$-noncollapsing and the proof of Proposition C

Part III. Long-time behaviour of Ricci flow with bubbling-off

  • The thin-thick decomposition theorem
  • Refined estimates for long-time behaviour

Part IV. Weak collapsing and hyperbolisation

  • Collapsing, simplicial volume and strategy of proof
  • Proof of the weak collapsing theorem
  • A rough classification of 3-manifolds
  • Appendix A. 3-manifold topology
  • Appendix B. Comparison geometry
  • Appendix C. Ricci flow
  • Appendix D. Alexandrov spaces
  • Appendix E. A sufficient condition for hyperbolicity
  • Bibliography
  • Index

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