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

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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.

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Authors and Affiliations

  1. Laboratoire J.A. Dieudonné, UMR du CNRS 6621, Université de Nice–Sophia Antipolis, Parc Valrose, 06108, Nice Cedex 02, France

    Alexandru Dimca

  2. Institute of Mathematics Simion Stoilow, P.O. Box 1-764, 014700, Bucharest, Romania

    Stefan Papadima

  3. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Alexander I. Suciu

Authors
  1. Alexandru Dimca
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  2. Stefan Papadima
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  3. Alexander I. Suciu
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Correspondence to Alexander I. Suciu.

Additional information

Alexandru Dimca and Stefan Papadima were partially supported by the French-Romanian Programme LEA Math-Mode. Alexandru Dimca was partially supported by ANR-08-BLAN-0317-02 (SÉDIGA).

Stefan Papadima was partially supported by CNCSIS grant ID-1189/2009-2011. Alexander I. Suciu was partially supported by NSA grant H98230-09-1-0012 and an ENHANCE grant from Northeastern University.

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Dimca, A., Papadima, S. & Suciu, A.I. Quasi-Kähler groups, 3-manifold groups, and formality. Math. Z. 268, 169–186 (2011). https://doi.org/10.1007/s00209-010-0664-y

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