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

In: Mathematica Slovaca, vol. 67, no. 3
Irina Gelbukh
Detaily:
Rok, strany: 2017, 645 - 656
Kľúčové slová:
co-rank, inner rank, manifold, fundamental group, direct product, Morse form foliation
O článku:
We study \$\b\$, 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 \$\b\$ and the first Betti number \$b1(M)\$ by explicitly constructing manifolds with any possible combination of \$\b\$ and \$b1(M)\$ in any given dimension. Finally, we apply our results to the topology of Morse form foliations. In particular, we construct a manifold \$M\$ and a Morse form \$\w\$ on it for any possible combination of \$\b\$, \$b1(M)\$, \$m(\w)\$, and \$c(\w)\$, where \$m(\w)\$ is the number of minimal components and \$c(\w)\$ is the maximum number of homologically independent compact leaves of \$\w\$.
Ako citovať:
ISO 690:
Gelbukh, I. 2017. The co-rank of the fundamental group: the direct product, the first Betti number, and the topology of foliations. In Mathematica Slovaca, vol. 67, no.3, pp. 645-656. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0298

APA:
Gelbukh, I. (2017). The co-rank of the fundamental group: the direct product, the first Betti number, and the topology of foliations. Mathematica Slovaca, 67(3), 645-656. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0298
O vydaní:
Publikované: 27. 6. 2017