Formulae for order one invariants of immersions and embeddings of surfaces

الأصل · EN

The universal order 1 invariant fᵘ of immersions of a closed orientable surface into R³, whose existence has been established in [N3], takes values in the group Gᵤ = K ⊕ Z/2 ⊕ Z/2 where K is a countably generated free Abelian group. The projections of fᵘ to K and to the first and second Z/2 factors are denoted fᵏ, M, Q respectively. An explicit formula for the value of Q on any embedding has been given in [N2]. In the present work we give an explicit formula for the value of fᵏ on any immersion, and for the value of M on any embedding.