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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 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 Gא0 ⊕B⊕B where Gא0 is the group of all functions from a set of cardinality א0 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. Mathamatics Subject Classification (2000): 57M, 57R42