2010/11/30 by D. Kotschick · 9 citations
Engineering · Mathematics · #Algebraic Geometry and Number Theory #Business #Combinatorics #Cyclic group #Engineering #Fundamental group #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Group (periodic table) #Kähler manifold #Manifold (fluid mechanics) #Mathematics #Order (exchange) #Philosophy #Physics #Product (mathematics) #Pure mathematics #Quantum mechanics #Simple (philosophy) #Topology (electrical circuits) #math.AG #math.CV #math.GR #math.GT #msc:14F35 #msc:32J15 #msc:32Q15 #msc:57M05 #msc:57M50
paper · pdf · doi:10.5802/aif.2717
published in Annales de l’institut Fourier 62(3), 1081-1090 (Association of the Annals of the Fourier Institute) · 6 pages; corrected statement of Theorem 6; final version to appear in Ann. Inst. Fourier
arxiv created 2011/02/12 · openalex publication_date 2012/01/01 · arxiv updated 2016/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℤ</mml:mi> </mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ℤ</mml:mi> <mml:mo>⊕</mml:mo> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> .