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تسجيل مستخدم جديدEmbeddings of $4$--manifolds in $CP^3$
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In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.
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This is a collection of notes on embedding problems for 3-manifolds. The main question explored is `which 3-manifolds embed smoothly in the 4-sphere? The terrain of exploration is the Burton/Martelli/Matveev/Petronio census of triangulated prime clos
ed 3-manifolds built from 11 or less tetrahedra. There are 13766 manifolds in the census, of which 13400 are orientable. Of the 13400 orientable manifolds, only 149 of them have hyperbolic torsion linking forms and are thus candidates for embedability in the 4-sphere. The majority of this paper is devoted to the embedding problem for these 149 manifolds. At present 41 are known to embed. Among the remaining manifolds, embeddings into homotopy 4-spheres are constructed for 4. 67 manifolds are known to not embed in the 4-sphere. This leaves 37 unresolved cases, of which only 3 are geometric manifolds i.e. having a trivial JSJ-decomposition.
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