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The space B0 i = Imm0(S1,R2)/ Diff(S1) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups &#960;1(B0 i) = Z, &#960;2(B0 i) = Z, and &#960;k(B0 i ) = 0 for k &#8805; 3.The space Bi = Imm0 (S 1 , R2 )/ Diff (S 1 ) of all immersions of rotation degree 0  0  0  in the plane modulo reparameterizations has homotopy groups 1 (Bi ) = Z,  0 0  2 (Bi ) = Z, and k (Bi ) = 0 for k 3

The Homotopy Type of the Space of Degree 0 — Immersed Plane Curves