Immersion extension-lift over a Morse function |
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Authors: | Minoru Yamamoto |
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Institution: | Department of Mathematics, Aichi University of Education, 1 Hirosawa, Igaya-cho, Kariya, Aichi, 448-8542, Japan |
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Abstract: | Let V be a compact connected oriented surface with boundary and f:∂V×0,1)→R a non-singular function such that f|∂V×{0} is a Morse function. Let ι:∂V×0,1)→V be a collaring of ∂V and π:R2→R an orthogonal projection. In this paper, we study existence of an orientation preserving immersion F:V→R2 such that π°F°ι=f. We also study image homotopy classes of F when we fix f and study relation between two image homotopy classes when f is deformed under a Morse homotopy. |
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Keywords: | primary 57R42 secondary 57R45 |
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