Mathematische Annalen

, Volume 328, Issue 1–2, pp 261–283 | Cite as

Order one invariants of immersions of surfaces into 3-space



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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityIsrael

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