Complementary regions for immersions of surfaces
Tahl Nowik
Abstract
Let F be a closed surface and i:F S3 a generic immersions. Then S3 - i(F) is a union of connected regions, which may be separated into two sets Uj and Vj by a checkerboard coloring. For k ≥ 0, let ak, bk be the number of components Uj, Vj with χ(Uj) = 1-k, χ(Vj)=1-k, respectively. Two more integers attached to i are the number N of triple points of i, and χ=χ(F). In this work we determine what sets of data (ak, bk, χ, N) may appear in this way.
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