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

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.

18 pages; accepted for publication in Mathematische Zeitschrift

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Topology and geometry of cohomology jump loci
• Which 3-manifold groups are Kähler groups?
• The boundary manifold of a complex line arrangement

Cited by in corpus (6)

• Fundamental groups, Alexander invariants, and cohomology jumping loci
• The topology of compact Lie group actions through the lens of finite models
• Co-rank and Betti number of a group
• Quasiprojective three-manifold groups and complexification of three-manifolds
• Finite Galois covers, cohomology jump loci, formality properties, and multinets
• Poincaré duality and resonance varieties