Quasi-K\"ahler groups, 3-manifold groups, and formality
Abstract
In this note, we address the following question: Which 1-formal groups occur as fundamental groups of both quasi-K\"ahler manifolds and closed, connected, orientable 3-manifolds. We classify all such groups, at the level of Malcev completions, and compute their coranks. Dropping the assumption on realizability by 3-manifolds, we show that the corank equals the isotropy index of the cup-product map in degree one. Finally, we examine the formality properties of smooth affine surfaces and quasi-homogeneous isolated surface singularities. In the latter case, we describe explicitly the positive-dimensional components of the first characteristic variety for the associated singularity link.
Cite
@article{arxiv.0810.2158,
title = {Quasi-K\"ahler groups, 3-manifold groups, and formality},
author = {Alexandru Dimca and Stefan Papadima and Alexander I. Suciu},
journal= {arXiv preprint arXiv:0810.2158},
year = {2011}
}
Comments
18 pages; accepted for publication in Mathematische Zeitschrift