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Paper withdrawn. There is a gap in the proof of Proposition 4.3 (its conclusion ``d'o\`{u} la proposition.'' is incorrect). Therefore theorems 1.1 and 3.1, which were the main results of the paper, are not proved.

Algebraic Geometry · Mathematics 2007-05-23 G. Laumon , J. L. Waldspurger

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

Combinatorics · Mathematics 2007-10-09 Robert Parviainen

This paper is being withdrawn because an error was discovered in lemma 4.3. Although the rest of the paper appears to be correct, this error invalidates the proof of theorem 3.1 and theorem 3.3.

Metric Geometry · Mathematics 2007-05-23 Lewis Bowen

The paper was withdrawn due to a gap in the proof of Lemma 3.

Symplectic Geometry · Mathematics 2007-05-23 H. Endo , D. Kotschick

This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.

Spectral Theory · Mathematics 2007-05-23 Raphael Ponge

The paper is withdrawn due to some errors.

Algebraic Topology · Mathematics 2012-02-17 Boris Botvinnik , Christine Escher

The paper is withdrawn. The proof has an error and it requires a different approach.

Dynamical Systems · Mathematics 2020-04-16 Robert Szalai

This paper has been withdrawn as the proof of Lemma 4.1 is incomplete.

Complex Variables · Mathematics 2016-09-09 Dusty Grundmeier , Jiri Lebl

This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.

Differential Geometry · Mathematics 2008-06-10 Jon Wolfson

This paper has been withdrawn by the author, as the proof of Theorem 3.2 contains a flaw; subsequently, both it and Theorem 3.3 are not known to hold. The content of Section 5 has been improved and expanded upon in two separate papers. The…

Geometric Topology · Mathematics 2011-01-18 Loretta Bartolini , J. Hyam Rubinstein

This paper is withdrawn because of an error in Lemma 3.1

Analysis of PDEs · Mathematics 2009-04-13 Shiva Shankar

Paper withdrawn due to errors (superseded by math.AG/0604303). Proposition 11.4 is false, Section 12 is false, and the main statement is true only for bundles $B$ with $c_1(B)$ SU(2)-invariant.

Algebraic Geometry · Mathematics 2007-05-23 Misha Verbitsky

This paper is withdrawn. We found a mistake in Lemma 4.1

Functional Analysis · Mathematics 2007-10-01 Marius Junge , Quanhua Xu

This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.

Differential Geometry · Mathematics 2007-05-23 Hong Huang

The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.

Algebraic Geometry · Mathematics 2007-05-23 Stefan Schroeer

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

High Energy Physics - Theory · Physics 2015-05-13 Chang-Yong Liu

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

Combinatorics · Mathematics 2008-04-14 S. Brlek , G. Labelle , A. Lacasse

This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.

Commutative Algebra · Mathematics 2007-05-23 Guillaume Rond

This paper has been withdrawn by the author due to a crucial error in the proof of Lemma 2.2.

Differential Geometry · Mathematics 2009-03-20 Zuoliang Hou , Xi-Nan Ma , Damin Wu

The paper has been withdrawn because the proof of part (b) of the main theorem is incomplete.

Algebraic Geometry · Mathematics 2009-07-29 Edoardo Sernesi
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