We explicitly calculate the fundamental group of the space F of
all immersed closed curves on a surface F. It is shown that Οnβ(F)=0, n>1 for Fξ =S2,RP2. It is also proved that Ο2β(F)=Z, and Οnβ(F)=Οnβ(S2)βΟn+1β(S2), n>2, for F
equal to S2 or RP2.Comment: 8 pages, 1 figure This paper will appear in Math. Scand. probably in
Vol. 86, no. 1, 200