The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations

@article{Gelbukh2015TheCO,
  title={The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations},
  author={Irina Gelbukh},
  journal={Mathematica Slovaca},
  year={2015},
  volume={67},
  pages={645 - 656}
}
Abstract We study b1′ $b_{1}'$ (M), the co-rank of the fundamental group of a smooth closed connected manifold M. We calculate this value for the direct product of manifolds. We characterize the set of all possible combinations of b1′ $b_{1}'$ (M) and the first Betti number b1(M) by explicitly constructing manifolds with any possible combination of b1′ $b_{1}'$ (M) and b1(M) in any given dimension. Finally, we apply our results to the topology of Morse form foliations. In particular, we… Expand

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References

SHOWING 1-10 OF 38 REFERENCES
Co-rank and Betti number of a group
Cut numbers of 3-manifolds
Foliated eight-manifolds for M-theory compactification
1-formes fermées singulières et groupe fondamental
HEEGAARD SPLITTINGS AND SPLITTING HOMOMORPHISMS
...
1
2
3
4
...