Related papers: The Tits Alternative: An Elementary Exposition

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

This paper has been withdrawn by the author(s), due a crucial sign error in conclusion .

This paper has been withdrawn by the author, due a critical mistake on page 3.

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

This paper has been withdrawn by the author.

This paper has been withdrawn by the author due to a gap in the proof of the main result.

This paper has been withdrawn by the author due to its publication

This paper has been withdrawn by the author due a crucial error.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn by the author, due to an error in Proposition 2.2.

This paper has been withdrawn by the authors due to an error in the main theorem.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

This paper has been withdrawn.

This paper has been withdrawn.

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

This submission has been withdrawn at the request of the author.