Stable classification of 4-manifolds

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== Introduction ==
== Introduction ==
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Revision as of 10:10, 27 November 2010

The user responsible for this page is Matthias Kreck. No other user may edit this page at present.

This page has not been refereed. The information given here might be incomplete or provisional.

Contents

1 Introduction

In this page we report about the stable classification of 4-manifolds.

2 Construction and examples

We begin with the construction of manifolds which give many stable diffeomorphism types of 4-manifolds:

  • S^4
  • S^2 \times S^2
  • \CP^2
  • K:= \{x \in \CP^3 | \sum x_i^4 =0\}, the Kummer surface.

Let P=<g_1, \dots , g_n| r_1,\dots,r_m> be the presentation of a group \pi. Then we build a 2-dimensional complex X(P) by taking a wedge of n circles and attaching a 2-cell via each relation r_i. Then we thicken X(P) to a smooth compact manifold with boundary W(P) in \mathbb R^5 and consider its boundary denoted by M(P). For details and why this is well defined see Thickenings. M(P) is a smooth 4-manifold with fundamental group \pi and we add it to our list

  • M(P)




3 Invariants

...

4 Classification/Characterization

...

5 Further discussion

...

6 References

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