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

Alexandru Dimca (1) , Stefan Papadima , Alexander I. Suciu

1 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

Alexandru Dimca, Stefan Papadima, Alexander I. Suciu. Quasi-Kähler groups, 3-manifold groups, and formality. Mathematische Zeitschrift, 2011, 268 (1), pp.169-186. ⟨10.1007/s00209-010-0664-y⟩. ⟨hal-00940382⟩