Automorphisms and Embeddings of Surfaces and Quadruple Points of Regular Homotopies Tahl Nowik

@inproceedings{Nowik2002AutomorphismsAE,
  title={Automorphisms and Embeddings of Surfaces and Quadruple Points of Regular Homotopies Tahl Nowik},
  author={Tahl Nowik},
  year={2002}
}
Let F be a closed surface. If i, i′ : F → R3 are two regularly homotopic generic immersions, then it has been shown in [5] that all generic regular homotopies between i and i′ have the same number mod 2 of quadruple points. We denote this number by Q(i, i′) ∈ Z/2. For F orientable we show that for any generic immersion i : F → R3 and any diffeomorphism h : F → F such that i and i ◦ h are regularly homotopic, Q(i, i ◦ h) = ( rank(h∗ − Id) + (n + 1) (h) ) 

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