Embeddings of Surfaces into 3-space and Quadruple Points of Regular Homotopies
نویسنده
چکیده
Let F be a closed orientable surface. We give an explicit formula for the number mod 2 of quadruple points occurring in any generic regular homotopy between any two regularly homotopic embeddings e, e : F → R. The formula is in terms of homological data extracted from the two embeddings.
منابع مشابه
Automorphisms and Embeddings of Surfaces and Quadruple Points of Regular Homotopies
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 regula...
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