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- Title
Quasi-Kähler groups, 3-manifold groups, and formality.
- Authors
Dimca, Alexandru; Papadima, Stefan; Suciu, Alexander I.
- Abstract
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.
- Subjects
FORMAL groups; GROUP schemes (Mathematics); FUNDAMENTAL groups (Mathematics); MANIFOLDS (Mathematics); THREE-manifolds (Topology)
- Publication
Mathematische Zeitschrift, 2011, Vol 268, Issue 1/2, p169
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-010-0664-y