الفهرس 
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Abstract
The word ”topology” is derived from two Greek words,”topos” meaning ”location” and ”logos” meaning ”study” and thus, the word topology literally means the study of location or position. The definitions and results of knot theory are briefly reviewed. Developing the necessary background of knots. The theory of mathematical braids, in both points of view of geometry and group theory is given. Also, we give an application of the inversion matrix on Baxter permutation. A General form of Rossler positive knot which has a braid representation is given. we have to clarify the relationship between knot theory and biology (DNA).