Homotopy Groups of the Space of Curves on a Surface
Abstract
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 $RP^2$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:math/9906123
 Bibcode:
 1999math......6123T
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Differential Geometry;
 53C42;
 57M99 (Primary)
 EPrint:
 8 pages, 1 figure This paper will appear in Math. Scand. probably in Vol. 86, no. 1, 2000