## 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.

### MSC:

 14F35 Homotopy theory and fundamental groups in algebraic geometry

### Keywords:

co-rank; fundamental group; manifold; foliation
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