Related papers: A calculus for shadows of smooth 4-manifolds

This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,

The paper has been withdrawn by the author.

This paper has been withdrawn by the author.

A shadowed polyhedron is a simple polyhedron equipped with half integers on regions, called gleams, which represents a compact, oriented, smooth 4-manifold. The polyhedron is embedded in the 4-manifold and it is called a shadow of that…

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

This paper has been withdrawn by the authors until some changes are made.

This paper has been withdrawn due to an incorrect analysis in Section 4.

This paper has been withdrawn by the author(s), due an error in the proof.

We prove that a closed 4-manifold has shadow-complexity zero if and only if it is a kind of 4-dimensional graph manifold, which decomposes into some particular blocks along embedded copies of S^2 x S^1, plus some complex projective spaces.…

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This paper has been withdrawn by the author due to a crucial error in equation.

This paper has been withdrawn by the author, due to the insecurity against attacks received in quant-ph/0605027v5.

This paper has been temporarily withdrawn for corrections.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

This paper has been withdrawn by the authors due to its publication

This paper is withdrawn by the author. See math.GT/9811093 for replacement.

This paper has been withdrawn due to disagreement of suggested results and methods between authors.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn due to a missing hypothesis in the main statement.

This paper has been withdrawn by the author.