SU(2) representations of the groups of integer tangles

Abstract

In this work we classify the irreducible SU(2) representations of $\Pi_1 (S^3\backslash k_n)$ where $k_n$ is an integer n tangle and as a result we have proved the following theorem: Let n be an odd integer then ${\cal R}$* $(\Pi_1 (S^3\backslash k_n)) /SO (3)$ is the disjoint union of n open arcs where ${\cal R}$* $\Pi_1 (S^3\backslash k_n))$ is the space of irreducible representations.

In this work we classify the irreducible SU(2) representations of $\Pi_1 (S^3\backslash k_n)$ where $k_n$ is an integer n tangle and as a result we have proved the following theorem: Let n be an odd integer then ${\cal R}$* $(\Pi_1 (S^3\backslash k_n)) /SO (3)$ is the disjoint union of n open arcs where ${\cal R}$* $\Pi_1 (S^3\backslash k_n))$ is the space of irreducible representations.