Area-preserving isotopies of self-transverse immersions of$S$^{1}in ℝ^{2}

Cecilia Karlsson Department of Mathematics, Uppsala University

Metric Geometry Symplectic Geometry mathscidoc:1701.23001

Arkiv for Matematik, 51, (1), 85-97, 2011.3
Let$C$and$C$′ be two smooth self-transverse immersions of$S$^{1}into ℝ^{2}. Both$C$and$C$′ subdivide the plane into a number of disks and one unbounded component. An isotopy of the plane which takes$C$to$C$′ induces a one-to-one correspondence between the disks of$C$and$C$′. An obvious necessary condition for there to exist an area-preserving isotopy of the plane taking$C$to$C$′ is that there exists an isotopy for which the area of every disk of$C$equals that of the corresponding disk of$C$′. In this paper we show that this is also a sufficient condition.
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@inproceedings{cecilia2011area-preserving,
  title={Area-preserving isotopies of self-transverse immersions of$S$^{1}in ℝ^{2}},
  author={Cecilia Karlsson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634974410039},
  booktitle={Arkiv for Matematik},
  volume={51},
  number={1},
  pages={85-97},
  year={2011},
}
Cecilia Karlsson. Area-preserving isotopies of self-transverse immersions of$S$^{1}in ℝ^{2}. 2011. Vol. 51. In Arkiv for Matematik. pp.85-97. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203634974410039.
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