Formulae for order one invariants of immersions and embeddings of surfaces
Tahl Nowik
Abstract
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.
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