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Item Details
| Title:
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SMOOTH FOUR-MANIFOLDS AND COMPLEX SURFACES
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| By: |
Robert Friedman, John W. Morgan |
| Format: |
Hardback |
| List price:
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£129.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3540570586 |
| ISBN 13: |
9783540570585 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
10 March, 1994 |
| Edition: |
1994 ed. |
| Series: |
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of 27 |
| Pages: |
522 |
| Description: |
Applies the techniques of gauge theory to study the smooth classification of compact complex surfaces. This book represents a marriage of the techniques of algebraic geometry and 4-manifold topology and gives an exposition of some of the main themes in this area of research. |
| Synopsis: |
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions. |
| Illustrations: |
X, 522 p. |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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Ramadan and Eid al-Fitr
A celebratory, inclusive and educational exploration of Ramadan and Eid al-Fitr for both children that celebrate and children who want to understand and appreciate their peers who do.
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