Full paper in PDF:
$%H. Kodama and P. W. Michor, The homotopy type of the space of degree 0 — Immersed plane curves, Rev. Mat. Complut. 19 (2006), no. 1, 227–234.%$

The Homotopy Type of the Space of Degree 0 — Immersed Plane Curves
Hiroki KODAMA and Peter W. MICHOR
Erwin Schrödinger Institut
für Mathematische Physik
Boltzmanngasse 9
A-1090 Wien — Austria
kodama@ms.u-tokyo.ac.jp
Fakultät für Mathematik
Universität Wien
Nordbergstrasse 15
A-1090 Wien — Austria
Peter.Michor@univie.ac.at

Received: October 25, 2005
Accepted: December 22, 2005
ABSTRACT

The space 0 0 1 2 1 B i = Imm (S ,R )/Diff(S ) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups 0 p1(B i)= Z , 0 p2(Bi)= Z , and 0 pk(B i) = 0 for k > 3 .

Key words: homotopy groups, immersed plane curves.
2000 Mathematics Subject Classification: Primary 58D10, 58D29, 55Q52.