Geometrisation of 3-Manifolds

  • Laurent Bessières

    Université Joseph Fourier, Grenoble, France
  • Gérard Besson

    Université Joseph Fourier, Grenoble, France
  • Michel Boileau

    Université Paul Sabatier, Toulouse, France
  • Sylvain Maillot

    Université Montpellier II, France
  • Joan Porti

    Universitat Autònoma de Barcelona, Spain
Geometrisation of 3-Manifolds cover

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FrontmatterDownload pp. i–iv
PrefaceDownload pp. v–vi
ContentsDownload pp. vii–x
1The Geometrisation Conjecturepp. 1–22
Part I Ricci flow with bubbling-off: definitions and statementsp. 23
2Basic definitionspp. 25–30
3Piecing together necks and capspp. 31–36
4-noncollapsing, canonical geometry and pinchingpp. 37–45
5Ricci flow with -bubbling-offpp. 46–56
Part II Ricci flow with bubbling-off: existencepp. 57–58
6Choosing cutoff parameterspp. 59–74
7Metric surgery and proof of Proposition App. 75–87
8Persistencepp. 88–96
9Canonical neighbourhoods and the proof of Proposition Bpp. 97–107
10-noncollapsing and the proof of Proposition Cpp. 108–129
Part III Long-time behaviour of Ricci flow with bubbling-offpp. 131–132
11The thin-thick decomposition theorempp. 133–145
12Refined estimates for long-time behaviourpp. 146–175
Part IV Weak collapsing and hyperbolisationpp. 177–178
13Collapsing, simplicial volume and strategy of proofpp. 179–187
14Proof of the weak collapsing theorempp. 188–206
15A rough classification of 3-manifoldspp. 207–208
A3-manifold topologypp. 209–212
BComparison geometrypp. 213–216
CRicci flowpp. 217–220
DAlexandrov spacesp. 221
EA sufficient condition for hyperbolicitypp. 222–223
Bibliographypp. 225–233
Indexpp. 235–237