CANCELLING CR SINGULARITIES OF 3 $3$ 3-MANIFOLDS IN COMPLEX THREEFOLDS

Abstract Let M be a closed oriented 3 $3$ 3 -manifold generically embedded in a complex 3 $3$ 3 -manifold X . Its CR singular set is an oriented link L ⊂ M $L\subset M$ upper L subset of upper M . We prove that if a sublink L ′ ⊂ L $L'\subset L$ upper L prime subset of upper L bounds an oriented Seifert surface S ⊂ M $S\subset M$ upper S subset of upper M in the complement of L ∖ L ′ $L\setminus L'$ upper L minus upper L prime , then the CR singularities along L ′ $L'$ upper L prime can be cancelled by an arbitrarily C 0 $\mathcal {C}^0$ script upper C Superscript 0 -small isotopy supported in an arbitrarily small neighbourhood of S .