(Co)homology of racks and multiple group racks for compact oriented surfaces in the 3-sphere

Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Knot theory (57K10) Generalized knots (virtual knots, welded knots, quandles, etc.) (57K12)

Cites Work

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A \(G\)-family of quandles and handlebody-knots
Homology for quandles with partial group operations
Inequivalent genus 2 handlebodies in \(S^ 3\) with homeomorphic complement
Cocycles of \(G\)-Alexander biquandles and \(G\)-Alexander multiple conjugation biquandles
A multiple conjugation quandle and handlebody-knots
Foliations and genera of links
Incompressible surfaces in 2-bridge knot complements
A classifying invariant of knots, the knot quandle
Finding disjoint incompressible spanning surfaces for a link
On the subdivision of 3-space by a polyhedron.
A multiple conjugation biquandle and handlebody-links
Biquandles and virtual links
Trunks and classifying spaces
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Neuwirtsche Knoten und Flächenabbildungen
The 3-cocycles of the Alexander quandles \(\mathbb F_q[T/(T-\omega)\)]
Augmented biracks and their homology
The Markov theorems for spatial graphs and handlebody-knots with Y-orientations
DISTRIBUTIVE GROUPOIDS IN KNOT THEORY
Knots are Determined by Their Complements
RACKS AND LINKS IN CODIMENSION TWO
Quandle cohomology and state-sum invariants of knotted curves and surfaces
State-sum invariants of knotted curves and surfaces from quandle cohomology
Partially multiplicative biquandles and handlebody-knots
Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles
AN INFINITE FAMILY OF NON-INVERTIBLE SURFACES IN 4-SPACE
Biquandle (co)homology and handlebody-links
A diagrammatic presentation and its characterization of non-split compact surfaces in the 3-sphere
A multiple group rack and oriented spatial surfaces
Piecewise Linear Isotopy and Embedding of Elements and Spheres (I)
Quandle homology groups, their Betti numbers, and virtual knots

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