%0 Journal Article %1 Suciu:mz10 %A Dimca, Alexandru %A Papadima, Stefan %A Suciu, Alexander I. %D 2011 %J Mathematische Zeitschrift %K Alex myown %N 1 %P 169-186 %R 10.1007/s00209-010-0664-y %T Quasi-Kähler groups, 3-manifold groups, and formality %U http://www.springerlink.com/content/q475773366186q08/ %V 268 %X In this note, we address the following question: Which 1-formal groups occur as fundamental groups of both quasi-Kähler 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.

@article{Suciu:mz10, abstract = {In this note, we address the following question: Which 1-formal groups occur as fundamental groups of both quasi-{K}{\"{a}}hler 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.}, added-at = {2010-01-30T19:33:22.000+0100}, arxiv = {http://arxiv.org/abs/0810.2158}, author = {Dimca, Alexandru and Papadima, Stefan and Suciu, Alexander I.}, biburl = {https://www.bibsonomy.org/bibtex/2794db06cf9735705c4f4a7f550b656d8/asuciu}, doi = {10.1007/s00209-010-0664-y}, interhash = {9e8750e278470d3b84c4e41b2585a0b6}, intrahash = {794db06cf9735705c4f4a7f550b656d8}, journal = {Mathematische Zeitschrift}, keywords = {Alex myown}, month = may, mrclass = {14F35, 20F34, 57N10(55N25,55P62)}, number = 1, pages = {169-186}, timestamp = {2012-02-05T15:08:28.000+0100}, title = {Quasi-{K}{\"{a}}hler groups, 3-manifold groups, and formality}, url = {http://www.springerlink.com/content/q475773366186q08/}, volume = 268, year = 2011 }