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

DOI10.1515/ms-2016-0298zbMath1424.14003arXiv1506.06300OpenAlexW2962841722MaRDI QIDQ5270926

Irina Gelbukh

Publication date: 3 July 2017

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.06300

zbMATH Keywords

manifoldfoliationfundamental groupco-rank

Mathematics Subject Classification ID

Homotopy theory and fundamental groups in algebraic geometry (14F35)

Related Items (10)

Loops in Reeb graphs of \(n\)-manifolds ⋮ Approximation of metric spaces by Reeb graphs: Cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannian manifolds ⋮ Reeb graphs of circle-valued functions: a survey and basic facts ⋮ Reeb spaces of smooth functions on manifolds II ⋮ Sufficient conditions for the compactifiability of~a~closed~one-form~foliation ⋮ Realization of a graph as the Reeb graph of a Morse function on a manifold ⋮ Compact and locally dense leaves of a closed one-form foliation ⋮ Combinatorial modifications of Reeb graphs and the realization problem ⋮ Morse-Bott functions with two critical values on a surface ⋮ A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function

Cites Work

• Quasi-Kähler groups, 3-manifold groups, and formality
• Groupe fondamental de l'espace des feuilles dans les feuilletages sans holonomie. (Fundamental group of the leaf space of foliations without holonomy)
• On codimension one foliations defined by closed one forms with singularities
• Local foliations and optimal regularity of Einstein spacetimes
• Sur l'unique ergodicité des 1-formes fermées singulières. (Unique ergodicity of closed singular 1-forms)
• 1-formes fermées singulières et groupe fondamental
• Foliated eight-manifolds for M-theory compactification
• Singular foliations for M-theory compactification
• Presence of minimal components in a Morse form foliation
• On the cut number of a \(3\)-manifold
• Geometric realizations for free quotients
• The co-rank conjecture for 3-manifold groups

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