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Extending immersed circles in the sphere to immersed disks in the ball

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Commentarii Mathematici Helvetici

Abstract

Consider a general position immersion of a circle into the 2-sphere. Suppose the immersion has an even number of double points. Then there is a proper immersion of the 2-disk that has the given curve as its boundary. Of all such extentions there is one with a minimum number of triple points. This minimum is obtained algorithmically in terms of a number that is associated to the double point set.

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Authors and Affiliations

  1. Department of Mathematics, University of South Alabama, 36688, Mobile, Alabama

    J. Scott Carter

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  1. J. Scott Carter
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Carter, J.S. Extending immersed circles in the sphere to immersed disks in the ball. Commentarii Mathematici Helvetici 67, 337–348 (1992). https://doi.org/10.1007/BF02566506

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  • DOI: https://doi.org/10.1007/BF02566506

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