Cancelling CR singularities of 3-manifolds in complex threefolds

Abstract

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