A \(G\)-family of quandles and handlebody-knots
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Publication:470861
zbMath1306.57011arXiv1205.1855MaRDI QIDQ470861
Masahide Iwakiri, Kanako Oshiro, Yeonhee Jang, Atsushi Ishii
Publication date: 13 November 2014
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1205.1855
Related Items (37)
New quantum invariants of theta-curves with base points ⋮ Cocycles of \(G\)-Alexander biquandles and \(G\)-Alexander multiple conjugation biquandles ⋮ Affine extensions of multiple conjugation quandles and augmented MCQ Alexander pairs ⋮ Handlebody-knots and development of quandle theory ⋮ A table of n-component handlebody links of genus n+1 up to six crossings ⋮ Geometric and homological considerations of local crossings of n-foams ⋮ Unknotting numbers for handlebody-knots and Alexander quandle colorings ⋮ The Markov theorems for spatial graphs and handlebody-knots with Y-orientations ⋮ Twisted cohomology pairings of knots. I: Diagrammatic computation ⋮ Tangle Machines ⋮ Derivatives with Alexander pairs for quandles ⋮ Rigidity and symmetry of cylindrical handlebody-knots ⋮ Extensions of augmented racks and surface ribbon cocycle invariants ⋮ A multiple conjugation quandle and handlebody-knots ⋮ Disingquandles and invariants of dichromatic singular links ⋮ On invariants of surfaces in the 3-sphere ⋮ On sufficiency of the definition of MCQ Alexander pairs in terms of invariants for handlebody-knots ⋮ Cohomology pairings of 3-manifolds and their diagrammatic computation ⋮ Twisted cohomology pairings of knots. III: Triple cup products ⋮ A multiple group rack and oriented spatial surfaces ⋮ Quandle cocycles from invariant theory ⋮ The Gordian distance of handlebody-knots and Alexander biquandle colorings ⋮ Continuous cohomology of topological quandles ⋮ Quandle identities and homology ⋮ Partially multiplicative biquandles and handlebody-knots ⋮ Diquandles and invariants for oriented dichromatic links ⋮ The tunnel number and the cutting number with constituent handlebody-knots ⋮ Twist spinning knotted trivalent graphs ⋮ Finitely stable racks and rack representations ⋮ Biquandle (co)homology and handlebody-links ⋮ Unknotting annuli and handlebody-knot symmetry ⋮ Qualgebras and knotted 3-valent graphs ⋮ Linear extensions of multiple conjugation quandles and MCQ Alexander pairs ⋮ Quantum invariants of framed links from ternary self-distributive cohomology ⋮ Higher arity self-distributive operations in Cascades and their cohomology ⋮ Distributivity versus associativity in the homology theory of algebraic structures ⋮ G-family polynomials
Cites Work
- Inequivalent handlebody-knots with homeomorphic complements
- Inequivalent genus 2 handlebodies in \(S^ 3\) with homeomorphic complement
- Moves and invariants for knotted handlebodies
- A classifying invariant of knots, the knot quandle
- Trunks and classifying spaces
- Quandle cocycles from invariant theory
- Quandle Cocycle Invariants for Spatial Graphs and Knotted Handlebodies
- Homology groups of symmetric quandles and cocycle invariants of links and surface-links
- A TABLE OF GENUS TWO HANDLEBODY-KNOTS UP TO SIX CROSSINGS
- SYMMETRIC QUANDLE COLORINGS FOR SPATIAL GRAPHS AND HANDLEBODY-LINKS
- The rack space
- Quandle cohomology and state-sum invariants of knotted curves and surfaces
- GEOMETRIC INTERPRETATIONS OF QUANDLE HOMOLOGY
- Quandle homology groups, their Betti numbers, and virtual knots
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