Mathematics – Geometric Topology
Scientific paper
1999-06-18
Math. Scand. 86 (2000), no. 1, 36--44.
Mathematics
Geometric Topology
8 pages, 1 figure This paper will appear in Math. Scand. probably in Vol. 86, no. 1, 2000
Scientific paper
We explicitly calculate the fundamental group of the space $\mathcal F$ of
all immersed closed curves on a surface $F$. It is shown that $\pi_n(\mathcal
F)=0$, n>1 for $F\neq S^2, RP^2$. It is also proved that $\pi_2(\mathcal
F)=\Z$, and $\pi_n(\mathcal F)=\pi_n(S^2)\oplus\pi_{n+1}(S^2)$, n>2, for $F$
equal to $S^2$ or $RP^2$.
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