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Canceling branch points on projections of surfaces in 4-space

Canceling branch points on projections of surfaces in 4-space

A surface embedded in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4"> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding="application/x-tex">4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space projects to a generic map in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding="application/x-tex">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space that may have branch points—each contributing <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="plus-or-minus 1"> <mml:semantics> <mml:mrow> <mml:mo>±<!-- ± …