Embeddings of Surfaces into 3-Space and Quadruple Points of Regular Homotopies
Tahl Nowik
Abstract
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 -> R3. The formula is in terms of homological data extracted from the two embeddings.
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