Geometric Structures on Manifolds (Graduate Studies in Mathematics, 227) - Softcover

Goldman, William M.

9781470471989: Geometric Structures on Manifolds (Graduate Studies in Mathematics, 227)

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ISBN 10: 1470471981 ISBN 13: 9781470471989

Verlag: American Mathematical Society, 2023

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Goldman explores geometric structures on manifolds locally modeled on a classical geometry. This area mediates between topology and geometry, he says, where a fixed topology is given a local coordinate system in the geometry of a homogeneous space of a Lie group. He surveys this theory with a special emphasis on affine and projective geometry. He has tried to keep prerequisites down to a minimum: beginning graduate courses in topology, differential geometry and algebra. Annotation �2022 Ringgold, Inc., Portland, OR (protoview.com)

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William M. Goldman, University of Maryland, College Park, MD.

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Verlag: American Mathematical Society
Erscheinungsdatum: 2023
Sprache: Englisch
ISBN 10: 1470471981
ISBN 13: 9781470471989
Einband: Taschenbuch
Anzahl der Seiten: 409
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Geometric Structures on Manifolds (eng)

William M. Goldman

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GEOMETRIC STRUCTURES ON MANIFOLDS

William M. Goldman

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Geometric Structures on Manifolds

Goldman, William M.

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Geometric Structures on Manifolds

William M. Goldman

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Geometric Structures on Manifolds (Paperback)

William M. Goldman

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ISBN 10: 1470471981 ISBN 13: 9781470471989

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Paperback. Zustand: new. Paperback. The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied previously. Such locally homogeneous geometric structures are special cases of Cartan connections where the associated curvature vanishes. This theory received a big boost in the 1970s when W. Thurston put his geometrization program for 3-manifolds in this context. The subject of this book is more ambitious in scope. Unlike Thurston's eight 3-dimensional geometries, it covers structures which are not metric structures, such as affine and projective structures.This book describes the known examples in dimensions one, two and three. Each geometry has its own special features, which provide special tools in its study. Emphasis is given to the inter-relationships between different geometries and how one kind of geometric structure induces structures modeled on a different geometry. Up to now, much of the literature has been somewhat inaccessible and the book collects many of the pieces into one unified work. This book focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a ""moduli space"". Often the moduli space carries a rich geometry of its own reflecting the model geometry.The book is self-contained and accessible to students who have taken first-year graduate courses in topology, smooth manifolds, differential geometry and Lie groups. Focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a moduli space. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verk�ufers 9781470471989

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Geometric Structures on Manifolds

William M. Goldman

Verlag: American Mathematical Society, US, 2023

ISBN 10: 1470471981 ISBN 13: 9781470471989

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Anbieter: Rarewaves.com USA, London, LONDO, Vereinigtes K�nigreich

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Paperback. Zustand: New. The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied previously. Such locally homogeneous geometric structures are special cases of Cartan connections where the associated curvature vanishes. This theory received a big boost in the 1970s when W. Thurston put his geometrization program for 3-manifolds in this context. The subject of this book is more ambitious in scope. Unlike Thurston's eight 3-dimensional geometries, it covers structures which are not metric structures, such as affine and projective structures.This book describes the known examples in dimensions one, two and three. Each geometry has its own special features, which provide special tools in its study. Emphasis is given to the inter-relationships between different geometries and how one kind of geometric structure induces structures modeled on a different geometry. Up to now, much of the literature has been somewhat inaccessible and the book collects many of the pieces into one unified work. This book focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a ""moduli space"". Often the moduli space carries a rich geometry of its own reflecting the model geometry.The book is self-contained and accessible to students who have taken first-year graduate courses in topology, smooth manifolds, differential geometry and Lie groups. Bestandsnummer des Verk�ufers LU-9781470471989

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