Gelbukh, Irina The co-rank of the fundamental group: the direct product, the first Betti number, and the topology of foliations. (English) Zbl 1424.14003 Math. Slovaca 67, No. 3, 645-656 (2017). The co-rank of a group \(G\) is the maximum rank of a free homomorphic image of \(G\). When \(G\) is the fundamental group of a connected manifold \(M\), the corresponding co-rank is denoted by \(b_1'(M)\). The author studies the relation of the co-rank \(b_1'(M)\) to the first Betti number \(b_1(M)\) of the manifold \(M\), to the direct product of two manifolds \(M_1 \times M_2\), and to invariants of Morse form foliations. Reviewer: Alexandru Dimca (Nice) Cited in 8 Documents MSC: 14F35 Homotopy theory and fundamental groups in algebraic geometry Keywords:co-rank; fundamental group; manifold; foliation PDF BibTeX XML Cite \textit{I. Gelbukh}, Math. Slovaca 67, No. 3, 645--656 (2017; Zbl 1424.14003) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.