The co-rank conjecture for 3-manifold groups

DOI10.2140/agt.2002.2.37zbMath0983.57001arXivmath/0202261OpenAlexW2138296054WikidataQ123186431 ScholiaQ123186431MaRDI QIDQ5954970

Christopher J. Leininger, Alan W. Reid

Publication date: 7 February 2002

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0202261

zbMATH Keywords

3-manifold groupco-rank of a groupcut-number

Mathematics Subject Classification ID

Geometric group theory (20F65) General geometric structures on low-dimensional manifolds (57M50) Fundamental group, presentations, free differential calculus (57M05) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (15)

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 ⋮ Co-rank and Betti number of a group ⋮ Reeb graphs of circle-valued functions: a survey and basic facts ⋮ Realization of a digraph as the Reeb graph of a Morse-Bott function on a given surface ⋮ Group trisections and smooth 4-manifolds ⋮ Cut numbers of 3-manifolds ⋮ Quasi-Kähler groups, 3-manifold groups, and formality ⋮ Integral lattices in TQFT ⋮ Quotients of mapping class groups from 𝑂𝑢𝑡(𝐹_{𝑛}) ⋮ Morse-Bott functions with two critical values on a surface ⋮ On the cut number of a \(3\)-manifold ⋮ A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function ⋮ Handlebody bundles and polytopes ⋮ The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations

Cites Work

• Algorithmic compression of surface automorphisms
• Hyperbolic 3-manifolds and surface automorphisms
• Reducing Heegaard splittings
• Integral points on character varieties
• On the cut number of a \(3\)-manifold
• Cobordism of automorphisms of surfaces
• On the geometry and dynamics of diffeomorphisms of surfaces
• Quadratic Forms and the Birman-Craggs Homomorphisms
• The μ-Invariant of 3-Manifolds and Certain Structural Properties of the Group of Homeomorphisms of a Closed, Oriented 2-Manifold
• Cut numbers of 3-manifolds
• 3-manifolds as viewed from the curve complex
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