4-manifolds: 1-connected
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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. | 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 [[ | + | It appears that the [[Intersection_form|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. | 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. | ||
Revision as of 10:48, 8 June 2010
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
3 Invariants
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4 Classification/Characterization
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5 Further discussion
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6 References
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This page has not been refereed. The information given here might be incomplete or provisional. |
