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Mohammad Ghomi
Mohammad Ghomi
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It sounds like, to some extent, what you are asking is whether an immersed closed curve in the plane can be extended to an immersion of a disk. This would yield the multiplicities that you seek; however, such an extension is not always possible. Necessary and sufficient conditions were fistfirst given in the thesis of Blank in 1967. For instance see this paper for more on this topic and references.

It sounds like, to some extent, what you are asking is whether an immersed closed curve in the plane can be extended to an immersion of a disk. This would yield the multiplicities that you seek; however, such an extension is not always possible. Necessary and sufficient conditions were fist given in the thesis of Blank in 1967. For instance see this paper for more on this topic and references.

It sounds like, to some extent, what you are asking is whether an immersed closed curve in the plane can be extended to an immersion of a disk. This would yield the multiplicities that you seek; however, such an extension is not always possible. Necessary and sufficient conditions were first given in the thesis of Blank in 1967. For instance see this paper for more on this topic and references.

Source Link
Mohammad Ghomi
Mohammad Ghomi
  • 7.2k
  • 1
  • 29
  • 54

It sounds like, to some extent, what you are asking is whether an immersed closed curve in the plane can be extended to an immersion of a disk. This would yield the multiplicities that you seek; however, such an extension is not always possible. Necessary and sufficient conditions were fist given in the thesis of Blank in 1967. For instance see this paper for more on this topic and references.