相关论文: An invariant for flat virtual knots

This paper has been withdrawn by the author, due an error in claim 1.

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The paper was withdrawn by the author. It contained various errors.

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The aim of the present paper is to construct series of invariants of free knots (flat virtual knots, virtual knots) valued in free groups (and also free products of cyclic groups). (Some minor mistakes are corrected)

This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.

This paper has been withdrawn by the author due to an error.

Paper withdrawn due to error.

This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

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This paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn by the author, due to errors in the figures.

This paper has been withdrawn by the author, due a crucial error in the main idea.

The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper has been withdrawn by the author due to a error in attachment of source file.

This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2