Embeddings of Surfaces into 3-Space and Quadruple Points of Regular Homotopies

Details Embeddings of Surfaces into 3-Space and Quadruple Points of Regular Homotopies Embeddings of Surfaces into 3-Space and Quadruple Points of Regular Homotopies

1999-11-10

arxiv.org/abs/math/9911066v1

Mathematics

Geometric Topology

11 pages, 2 figures

Scientific paper

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^3. The formula is in
terms of homological data extracted from the two embeddings.

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