Alexander Polynomial of a Knot
A detailed guide to alexander polynomial of a knot. Covers key methods, mathematical significance, and real-world applications.
Mathematics Category
Knot Theory
50 articles
≈ 500 min total reading
Alternating Knots and Tait Conjectures
A detailed guide to alternating knots and tait conjectures. Covers key methods, mathematical significance, and real-world applications.
Braid Group Representations and Knots
A detailed guide to braid group representations and knots. Covers key methods, mathematical significance, and real-world applications.
Bridge Number and Knot Complexity
A detailed guide to bridge number and knot complexity. Covers key methods, mathematical significance, and real-world applications.
Crossing Number of Knots and Links
A detailed guide to crossing number of knots and links. Covers key methods, mathematical significance, and real-world applications.
Dtbled Knots and Cosmetic Surgery
A detailed guide to dtbled knots and cosmetic surgery. Covers key methods, mathematical significance, and real-world applications.
Fibered Knots and Monodromy
A detailed guide to fibered knots and monodromy. Covers key methods, mathematical significance, and real-world applications.
Framed Links and Three Manifold Construction
A detailed guide to framed links and three manifold construction. Covers key methods, mathematical significance, and real-world applications.
Higher Dimensional Knot Embeddings
A detailed guide to higher dimensional knot embeddings. Covers key methods, mathematical significance, and real-world applications.
Hyperbolic Knots and Thurston Geometrization
A detailed guide to hyperbolic knots and thurston geometrization. Covers key methods, mathematical significance, and real-world applications.
Jones Polynomial and Quantum Invariants
A detailed guide to jones polynomial and quantum invariants. Covers key methods, mathematical significance, and real-world applications.
Kauffman Bracket and State Sum Models
A detailed guide to kauffman bracket and state sum models. Covers key methods, mathematical significance, and real-world applications.
Khovanov Homology and Categorification
A detailed guide to khovanov homology and categorification. Covers key methods, mathematical significance, and real-world applications.
Knot Colored Invariants and Representations
A detailed guide to knot colored invariants and representations. Covers key methods, mathematical significance, and real-world applications.
Knot Complement and Topology
A detailed guide to knot complement and topology. Covers key methods, mathematical significance, and real-world applications.
Knot Concordance and Genus Bounds
A detailed guide to knot concordance and genus bounds. Covers key methods, mathematical significance, and real-world applications.
Knot Concordance Group Structure
A detailed guide to knot concordance group structure. Covers key methods, mathematical significance, and real-world applications.
Knot Definition and Equivalence by Isotopy
A detailed guide to knot definition and equivalence by isotopy. Covers key methods, mathematical significance, and real-world applications.
Knot Energies and Ideal Configurations
A detailed guide to knot energies and ideal configurations. Covers key methods, mathematical significance, and real-world applications.
Knot Group and Fundamental Group
A detailed guide to knot group and fundamental group. Covers key methods, mathematical significance, and real-world applications.
Knot Invariants from Floer Homology
A detailed guide to knot invariants from floer homology. Covers key methods, mathematical significance, and real-world applications.
Knot Invariants from Quantum Computing
A detailed guide to knot invariants from quantum computing. Covers key methods, mathematical significance, and real-world applications.
Knot Invariants from Representations
A detailed guide to knot invariants from representations. Covers key methods, mathematical significance, and real-world applications.
Knot Moser Type Results and Embedded Tori
A detailed guide to knot moser type results and embedded tori. Covers key methods, mathematical significance, and real-world applications.
Knot Polynomials and Chromatic Invariants
A detailed guide to knot polynomials and chromatic invariants. Covers key methods, mathematical significance, and real-world applications.
Knot Projections and Regular Diagrams
A detailed guide to knot projections and regular diagrams. Covers key methods, mathematical significance, and real-world applications.
Knot Symmetries and Invertibility Properties
A detailed guide to knot symmetries and invertibility properties. Covers key methods, mathematical significance, and real-world applications.
Knot Tabulation and Classification Efforts
A detailed guide to knot tabulation and classification efforts. Covers key methods, mathematical significance, and real-world applications.
Knot Theorists and Historical Development
A detailed guide to knot theorists and historical development. Covers key methods, mathematical significance, and real-world applications.
Knot Theory Applications in Biology
A detailed guide to knot theory applications in biology. Covers key methods, mathematical significance, and real-world applications.
Knotoids and Open Curve Invariants
A detailed guide to knotoids and open curve invariants. Covers key methods, mathematical significance, and real-world applications.
Knots in Four Dimensions and Higher
A detailed guide to knots in four dimensions and higher. Covers key methods, mathematical significance, and real-world applications.
Knots in Lens Spaces and Manifolds
A detailed guide to knots in lens spaces and manifolds. Covers key methods, mathematical significance, and real-world applications.
Lattice Knots and Discrete Models
A detailed guide to lattice knots and discrete models. Covers key methods, mathematical significance, and real-world applications.
Link Homology and Categorification Theories
A detailed guide to link homology and categorification theories. Covers key methods, mathematical significance, and real-world applications.
Linking Number and Two Component Links
A detailed guide to linking number and two component links. Covers key methods, mathematical significance, and real-world applications.
Prime Decomposition of Knots
A detailed guide to prime decomposition of knots. Covers key methods, mathematical significance, and real-world applications.
Reidemeister Moves on Knot Diagrams
A detailed guide to reidemeister moves on knot diagrams. Covers key methods, mathematical significance, and real-world applications.
Ribbon Knots and Slice Problem
A detailed guide to ribbon knots and slice problem. Covers key methods, mathematical significance, and real-world applications.
Seifert Surfaces and Genus of Knots
A detailed guide to seifert surfaces and genus of knots. Covers key methods, mathematical significance, and real-world applications.
Skein Relations for Knot Polynomials
A detailed guide to skein relations for knot polynomials. Covers key methods, mathematical significance, and real-world applications.
Spatial Graphs and Knotted Structures
A detailed guide to spatial graphs and knotted structures. Covers key methods, mathematical significance, and real-world applications.
Surgery Theory and Dehn Filling
A detailed guide to surgery theory and dehn filling. Covers key methods, mathematical significance, and real-world applications.
Thick Embeddings and Knot Width
A detailed guide to thick embeddings and knot width. Covers key methods, mathematical significance, and real-world applications.
Torus Knots and Their Classification
A detailed guide to torus knots and their classification. Covers key methods, mathematical significance, and real-world applications.
Tricolorability and Knot Invariants
A detailed guide to tricolorability and knot invariants. Covers key methods, mathematical significance, and real-world applications.
Unknotting Number and Crossing Changes
A detailed guide to unknotting number and crossing changes. Covers key methods, mathematical significance, and real-world applications.
Virtual Knots and Generalized Knot Theory
A detailed guide to virtual knots and generalized knot theory. Covers key methods, mathematical significance, and real-world applications.
Writhing Number and Framed Links
A detailed guide to writhing number and framed links. Covers key methods, mathematical significance, and real-world applications.
Writhing of Knots and Rotation Number
A detailed guide to writhing of knots and rotation number. Covers key methods, mathematical significance, and real-world applications.