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Extending Closed Plane Curves to Immersions of the Disk with n Handles

1975
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Transactions of the American Mathematical Society
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Let /: S -► E be a normal curve In the plane. The extensions of / to immersions of the disk with n handles (Tn) can be determined as follows. A word for / is constructed using the definitions of Blank and Marx and a combinatorial structure, called a ^-assemblage, is defined for such words. There is an immersion extending / to Tn iff the tangent winding number of / is 1 -2/t and / has a ^-assemblage. For each n, a canonical curve /" with a topologically unique extension to Tn is described (/q =

doi:10.2307/1997145
fatcat:aajqsg3qmbachmlfnv2qn6267i