Critical sets in 3-space

Matthew Grayson; Charles Pugh

doi:10.1007/BF02699187

Publications Mathématiques de l'Institut des Hautes Scientifiques

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01 Dec 1993

Critical sets in 3-space

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Abstract

Given a non-empty compact set C ⊂R 3, is C the set of critical points for some smooth proper function f 3 →R +? In this paper we prove that the answer is "yes" for Antoine's Necklace and most but not all tame links. © 1993 Publications Mathématiques de L'I.É.E.S.

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