The co-rank of the fundamental group: the direct product, the first Betti number, and the topology of foliations. (English) Zbl 1424.14003

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.


14F35 Homotopy theory and fundamental groups in algebraic geometry
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