TOPOLOGICAL PROPERTIES OF CYCLICALLY PRESENTED GROUPS

DOI10.1142/S021821650300241XzbMath1031.57002OpenAlexW2063649969MaRDI QIDQ4414987

Dušan D. Repovš, Fulvia Spaggiari, Alberto Cavicchioli

Publication date: 24 February 2004

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021821650300241x

zbMATH Keywords

manifoldbranched coveringknotisometry grouporbifoldhomologyhyperbolic structurecyclically presented groupsplit extensionhigh-dimensional knot groupnatural HNN extension

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Surgery and handlebodies (57R65) Fundamental group, presentations, free differential calculus (57M05) Low-dimensional topology of special (e.g., branched) coverings (57M12) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (22)

Fractional Fibonacci groups with an odd number of generators ⋮ LARGENESS AND SQ-UNIVERSALITY OF CYCLICALLY PRESENTED GROUPS ⋮ A Topological Study of Some Groups Arising from Cellular Quotients ⋮ Efficient finite groups arising in the study of relative asphericity ⋮ On the generalized Dunwoody 3-manifolds ⋮ Fibonacci type presentations and 3-manifolds ⋮ Algebras and groups defined by permutation relations of alternating type. ⋮ Universal presentations for manifold groups ⋮ Perfect Prishchepov groups ⋮ TORUS KNOTS AND 3-MANIFOLDS ⋮ Generalized Fibonacci groups \(H(r,n,s)\) that are connected labelled oriented graph groups ⋮ On some questions about a family of cyclically presented groups. ⋮ The cyclically presented groups with relators \(x_ix_{i+k}x_{i+l}\). ⋮ Families of group presentations related to topology ⋮ Combinatorics of a class of groups with cyclic presentation ⋮ The aspherical Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups ⋮ PALINDROME PRESENTATIONS OF RATIONAL KNOTS ⋮ ON THE CLASSIFICATION OF KIM AND KOSTRIKIN MANIFOLDS ⋮ Certain Cyclically Presented Groups with the Same Polynomial ⋮ On the topology of the groups of type \(\mathfrak{Z}\) ⋮ Isomorphism theorems for classes of cyclically presented groups ⋮ A geometric study of generalized Neuwirth groups

Cites Work

• Unnamed Item
• Combinatorial squashings, 3-manifolds, and the third homology of groups
• Neuwirth manifolds and colourings of graphs
• On cyclic branched coverings of torus knots
• Generalised Fibonacci manifolds
• LOG groups and cyclically presented groups
• Generalized Neuwirth Groups and Seifert Fibered Manifolds
• On infinite groups of Fibonacci type
• HIGH DIMENSIONAL KNOT GROUPS AND HNN EXTENSIONS OF THE FIBONACCI GROUPS
• Some diophantine problems arising from the theory of cyclically-presented groups
• Some results on symmetrically-presented groups
• The Euclidean Representations of the Fibonacci Groups
• ON THE ARITHMETIC 2-BRIDGE KNOTS AND LINK ORBIFOLDS AND A NEW KNOT INVARIANT
• Aspherisity, atorisity and simmetrically presented groups
• Some honey-combs in hyperbolic 3-space
• On generalized fibonacci groups with an odd number of generators

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