Homotopy Groups of the Space of Curves on a Surface
Abstract
Description
We explicitly calculate the fundamental group of the space $\mathcal F$ of all immersed closed curves on a surface $F$. It is shown that $π_n(\mathcal F)=0$, n>1 for $F\neq S^2, RP^2$. It is also proved that $π_2(\mathcal F)=\Z$, and $π_n(\mathcal F)=π_n(S^2)\oplusπ_{n+1}(S^2)$, n>2, for $F$ equal to $S^2$ or $RP^2$.
8 pages, 1 figure This paper will appear in Math. Scand. probably in Vol. 86, no. 1, 2000
8 pages, 1 figure This paper will appear in Math. Scand. probably in Vol. 86, no. 1, 2000