Classification of immersions of graphs into a plane |
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Authors: | D A Permyakov |
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Institution: | (1) Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia |
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Abstract: | In 2005, R. Nikkuni calculated the Wu invariant for immersions of graphs into a plane considered up to a regular homotopy, i.e., for homotopies that are immersions. He showed that two immersions are regularly homotopic if and only if their Wu invariants coincide. In this paper a simple combinatorial construction for this invariant is described, a theorem similar to Ryo Nikkuni’s theorem is proved, and the fact that all values of the constructed combinatorial invariant can be implemented by immersions is also proved. |
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