Order one invariants of immersions of surfaces into 3-space
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We classify all order one invariants of immersions of a closed orientable surface F into ℝ3, with values in an arbitrary Abelian group . We show that for any F and and any regular homotopy class of immersions of F into ℝ3, the group of all order one invariants on is isomorphic to is the group of all functions from a set of cardinality . Our work includes foundations for the study of finite order invariants of immersions of a closed orientable surface into ℝ3, analogous to chord diagrams and the 1-term and 4-term relations of knot theory.
KeywordsAbelian Group Homotopy Class Finite Order Orientable Surface Chord Diagram
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- 2.Goryunov, V.V.: Local Invariants of Mappings of Surfaces into Three-Space. Arnold-Gelfand Mathematical Seminars, Geometry and Singularity Theory. Birkhauser Boston Inc., 1997, pp. 223–255Google Scholar
- 5.Kontsevich, M.: Vassiliev’s knot invariants. I.M. Gelfand Seminar, Advances in Soviet Mathematics 16, Part 2, Am. Math. Soc., Providence, RI, 1993, pp. 137–150Google Scholar
- 6.Max, N.: Turning a sphere inside out, a guide to the film. Computers in Mathematics, Marcel Dekker Inc., 1990, pp. 334–345Google Scholar
- 7.Max, N., Banchoff, T.: Every Sphere Eversion Has a Quadruple Point. Contributions to Analysis and Geometry, John Hopkins University Press, 1981, pp. 191–209Google Scholar