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Abstract:
Consider the projection of the standard S2
to R2. This is a map with only one curve of fold singularities
(a fold curve). This map clearly extends to a non-singular map (ie a submersion) of
D3
Question: Does every map S2
to R2 with only one fold curve of singularities extend to a
submersion of D3?
We show the answer is "No" by giving a necessary condition and exhibiting a
counter-example. It turns out that this condition is also sufficient and we
give an easily computable (combinatoric) algorithm for determining exactly
when the condition holds.
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