In this work we classify the irreducible SU(2) representations of P1(S3\backslash kn) where kn is an integer n tangle and as a result we have proved the following theorem: Let n be an odd integer then \mathcal{R}\ast(P1(S3 \backslash kn)) /SO(3) is the disjoint union of n open arcs where \mathcal{R}\ast(P 1(S3 \backslash kn)) is the space of irreducible representations.

In this work we classify the irreducible SU(2) representations of P1(S3\backslash kn) where kn is an integer n tangle and as a result we have proved the following theorem: Let n be an odd integer then \mathcal{R}\ast(P1(S3 \backslash kn)) /SO(3) is the disjoint union of n open arcs where \mathcal{R}\ast(P 1(S3 \backslash kn)) is the space of irreducible representations.