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arXiv · 1601.07284

Area preserving isotopies of self transverse immersions of S^1 in R^2

Cecilia Karlsson
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Abstract

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 1-1 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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Cecilia Karlsson. 2016-01-27. Area preserving isotopies of self transverse immersions of S^1 in R^2. https://doi.org/10.1007/s11512-012-0165-9

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