Kasparian, Azniv Inequalities among the number of the generators and relations of a Kähler group. (English) Zbl 1005.57001 Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 3rd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 14-23, 2001. Sofia: Coral Press Scientific Publishing. 315-317 (2002). Summary: The present note announces some inequalities on the number of the generators and relations of a Kähler group \(\pi_1(X)\), involving the irregularity \(q(X)\), the Albanese dimension \(a(X)\) and the Albanese genera \(g_k(X)\), \(1\leq k\leq a(X)\), of the corresponding compact Kähler manifold \(X\). The principal ideas for their derivation are outlined and the proofs are postponed to be published elsewhere.For the entire collection see [Zbl 0980.00035]. MSC: 57M05 Fundamental group, presentations, free differential calculus 57R19 Algebraic topology on manifolds and differential topology 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32J27 Compact Kähler manifolds: generalizations, classification 55Q52 Homotopy groups of special spaces 55R40 Homology of classifying spaces and characteristic classes in algebraic topology 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 20J06 Cohomology of groups Keywords:fundamental group; Albanese variety; Albanese dimension; Albanese genera; Kähler manifold PDFBibTeX XMLCite \textit{A. Kasparian}, in: Proceedings of the 3rd international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 14--23, 2001. Sofia: Coral Press Scientific Publishing. 315--317 (2002; Zbl 1005.57001)