Quasi-Kähler groups, 3-manifold groups, and formality

Details Quasi-Kähler groups, 3-manifold groups, and formality Quasi-Kähler groups, 3-manifold groups, and formality

2008-10-13

arxiv.org/abs/0810.2158v3

Mathematische Zeitschrift 268 (2011), no. 1, 169-186

Mathematics

Algebraic Geometry

18 pages; accepted for publication in Mathematische Zeitschrift

Scientific paper

10.1007/s00209-010-0664-y

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.

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