Abstract

Let f : M→R² be a smooth immersion of a compact connected oriented surface with boundary M into R². Kauffman defined an equivalence relation called image homotopy and classified the set of all orientation preserving immersions of M into R² up to image homotopy. When M is of genus one and the number of boundary components is strictly greater than one, Kauffman’s result requires a correction. In this paper we will study this particular case.

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