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The Geometrization Conjecture
Af: John Morgan, Gang Tian Engelsk Hardback
SPAR
kr 61
The Geometrization Conjecture
Af: John Morgan, Gang Tian Engelsk Hardback
This book gives a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces, i.e., 3-manifolds with locally homogeneous metrics of finite volume. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric. This is established by showing that the Gromov-Hausdorff limits of sequences of more and more locally volume collapsed 3-manifolds are Alexandrov spaces of dimension at most 2 and then classifying these Alexandrov spaces. In the course of proving the geometrization conjecture, the authors provide an overview of the main results about Ricci flows with surgery on 3-dimensional manifolds, introducing the reader to this difficult material. The book also includes an elementary introduction to Gromov-Hausdorff limits and to the basics of the theory of Alexandrov spaces. In addition, a complete picture of the local structure of Alexandrov surfaces is developed. All of these important topics are of independent interest.
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This book gives a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces, i.e., 3-manifolds with locally homogeneous metrics of finite volume. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric. This is established by showing that the Gromov-Hausdorff limits of sequences of more and more locally volume collapsed 3-manifolds are Alexandrov spaces of dimension at most 2 and then classifying these Alexandrov spaces. In the course of proving the geometrization conjecture, the authors provide an overview of the main results about Ricci flows with surgery on 3-dimensional manifolds, introducing the reader to this difficult material. The book also includes an elementary introduction to Gromov-Hausdorff limits and to the basics of the theory of Alexandrov spaces. In addition, a complete picture of the local structure of Alexandrov surfaces is developed. All of these important topics are of independent interest.
Produktdetaljer
Sprog: Engelsk
Sider: 291
ISBN-13: 9780821852019
Indbinding: Hardback
Udgave:
ISBN-10: 0821852019
Kategori: Geometri
Udg. Dato: 30 maj 2014
Længde: 24mm
Bredde: 189mm
Højde: 263mm
Oplagsdato: 30 maj 2014
Forfatter(e): John Morgan, Gang Tian
Forfatter(e) John Morgan, Gang Tian


Kategori Geometri


Sprog Engelsk


Indbinding Hardback


Sider 291


Udgave


Længde 24mm


Bredde 189mm


Højde 263mm


Udg. Dato 30 maj 2014


Oplagsdato 30 maj 2014

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