Order One Invariants of Immersions

الأصل · EN

We classify all order one invariants of immersions of a closed orientable surface F into R³, with values in an arbitrary Abelian group G. We show that for any F and G and any regular homotopy class A of immersions of F into R³, the group of all order one invariants on A is isomorphic to G₀ ⊕ B ⊕ B where G₀ is the group of all functions from a set of cardinality ₀ into G and B=x∈ G: 2x=0. 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.