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

Research paper by Cecilia Karlsson

Indexed on: 27 Jan '16Published on: 27 Jan '16Published in: Mathematics - Symplectic Geometry



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.