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The folded ribbon theorem for regular closed curves in the plane

1968
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Bulletin of the American Mathematical Society
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Let 5 be the oriented circle with base point, E the oriented Euclidian plane, and V the positively oriented two frames in E. Let L be the space of D-regular immersions g: S-^E with continuous right transverse field |. For gGL, set dg= (g, g, g') : S-+EX V. A positive monotone regular homotopy ( = monotopy) from loop g_i to g+i is a C 1regular homotopy G: [•-1, + l]XS-*E with positive Jacobian and dG(i, x)=dgi(x), i = ±1, where öG=(G, dG/dt, dG/dx). A negative monotopy G from g_i to g+i is such

doi:10.1090/s0002-9904-1968-11914-7
fatcat:drsll5y4zjd3ximt5xwkdzodcy