4-manifolds: 1-connected
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== Introduction == | == Introduction == | ||
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=== First examples === | === First examples === | ||
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− | + | The first examples that come to one's mind are the 4-sphere $S^4$, the complex projective space $\mathbb{CP}^2$, the complex projective space with its opposite (non-complex) orientation $\overline{\mathbb{CP}^2}$, the product $S^2 \times S^2$, various connected sums of these, and in particular $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. | |
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[[Category:Manifolds]] | [[Category:Manifolds]] | ||
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Revision as of 11:19, 8 June 2010
This page has not been refereed. The information given here might be incomplete or provisional. |
Contents |
1 Introduction
Any finitely presentable group may occur as the fundamental group of a smooth closed 4-manifold. On the other hand, the class of simply connected (topological or smooth) 4-manifolds still appears to be quite rich, so it appears reasonable to consider the classification of simply connected 4-manifolds in particular.
It appears that the intersection form is the main algebro-topological invariant of simply-connected 4-manifolds.
Technical remark: When we mention the term 4-manifold without the explicit mention of topological or smooth we shall mean the larger class of topological 4-manifolds.
2 Construction and examples
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2.1 First examples
The first examples that come to one's mind are the 4-sphere , the complex projective space , the complex projective space with its opposite (non-complex) orientation , the product , various connected sums of these, and in particular .
3 Invariants
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4 Classification/Characterization
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5 Further discussion
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