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

Rok, strany: 2017, 645 - 656

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 $\w$.

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