Immersed 𝑛-manifolds in 𝐑²ⁿ and the double points of their generic projections into 𝐑²ⁿ⁻¹
Immersed 𝑛-manifolds in 𝐑²ⁿ and the double points of their generic projections into 𝐑²ⁿ⁻¹
We give two congruence formulas concerning the number of non-trivial double point circles and arcs of a smooth map with generic singularities—the Whitney umbrellas—of an <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifold into <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper R Superscript 2 n minus 1"> …