# FUNDAMENTAL GROUPS OF LINKS OF ISOLATED SINGULARITIES

## Author(s): Kapovich, Michael; Kollar, Janos

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 Abstract: We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group $G$ there is a complex projective surface $S$ with simple normal crossing singularities only, so that the fundamental group of $S$ is isomorphic to $G$. We use this to construct 3-dimensional isolated complex singularities so that the fundamental group of the link is isomorphic to $G$. Lastly, we prove that a finitely-presented group $G$ is ${\mathbb{Q}}$-superperfect (has vanishing rational homology in dimensions 1 and 2) if and only if $G$ is isomorphic to the fundamental group of the link of a rational 6-dimensional complex singularity. Publication Date: Oct-2014 Electronic Publication Date: 22-May-2014 Citation: Kapovich, Michael, Kollar, Janos. (2014). FUNDAMENTAL GROUPS OF LINKS OF ISOLATED SINGULARITIES. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 27 (929 - 952 ISSN: 0894-0347 EISSN: 1088-6834 Pages: 929 - 952 Type of Material: Journal Article Journal/Proceeding Title: JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Version: Author's manuscript