Formulae for order one invariants of immersions and embeddings of surfaces

Details Formulae for order one invariants of immersions and embeddings of surfaces Formulae for order one invariants of immersions and embeddings of surfaces

2003-05-05

arxiv.org/abs/math/0305070v1

Mathematics

Geometric Topology

Scientific paper

The universal order 1 invariant f^U of immersions of a closed orientable surface into R^3, whose existence has been established in [N3], takes values in the group G_U = K \oplus Z/2 \oplus Z/2 where K is a countably generated free Abelian group. The projections of f^U to K and to the first and second Z/2 factors are denoted f^K, 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 f^K on any immersion, and for the value of M on any embedding.

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