Alexander Polynomial and Knot Invariants
A detailed guide to alexander polynomial and knot invariants. Covers key methods, mathematical significance, and real-world applications.
Mathematics Category
Low Dim Topology
50 articles
≈ 500 min total reading
Alternating Knots and Tait Conjectures (Low Dim Topology)
A detailed guide to alternating knots and tait conjectures (low dim topology). Covers key methods, mathematical significance, and real-world applications.
Braid Groups and Knot Connections
A detailed guide to braid groups and knot connections. Covers key methods, mathematical significance, and real-world applications.
Bridge Number and Knot Complexity (Low Dim Topology)
A detailed guide to bridge number and knot complexity (low dim topology). Covers key methods, mathematical significance, and real-world applications.
Casson Invariant of Integer Homology Spheres
A detailed guide to casson invariant of integer homology spheres. Covers key methods, mathematical significance, and real-world applications.
Cobordism Between Manifolds of Low Dimension
A detailed guide to cobordism between manifolds of low dimension. Covers key methods, mathematical significance, and real-world applications.
Conway Notation and Tangle Calculus
A detailed guide to conway notation and tangle calculus. Covers key methods, mathematical significance, and real-world applications.
Crossing Number and Knot Tabulation
A detailed guide to crossing number and knot tabulation. Covers key methods, mathematical significance, and real-world applications.
Dehn Surgery on Knots in Three Manifolds
A detailed guide to dehn surgery on knots in three manifolds. Covers key methods, mathematical significance, and real-world applications.
Dehn Twists and Surface Homeomorphisms
A detailed guide to dehn twists and surface homeomorphisms. Covers key methods, mathematical significance, and real-world applications.
Handlebody Decompositions in Topology
A detailed guide to handlebody decompositions in topology. Covers key methods, mathematical significance, and real-world applications.
Hyperbolic Three Manifolds and Volumes
A detailed guide to hyperbolic three manifolds and volumes. Covers key methods, mathematical significance, and real-world applications.
Instanton Floer Homology of Three Manifolds
A detailed guide to instanton floer homology of three manifolds. Covers key methods, mathematical significance, and real-world applications.
Jones Polynomial of a Knot
A detailed guide to jones polynomial of a knot. Covers key methods, mathematical significance, and real-world applications.
JSJ Decomposition of Three Manifolds
A detailed guide to jsj decomposition of three manifolds. Covers key methods, mathematical significance, and real-world applications.
Khovanov Homology of Links
A detailed guide to khovanov homology of links. Covers key methods, mathematical significance, and real-world applications.
Kirby Calculus and Surgery Descriptions
A detailed guide to kirby calculus and surgery descriptions. Covers key methods, mathematical significance, and real-world applications.
Knot Complements and Hyperbolic Geometry
A detailed guide to knot complements and hyperbolic geometry. Covers key methods, mathematical significance, and real-world applications.
Knot Concordance Group Structure (Low Dim Topology)
A detailed guide to knot concordance group structure (low dim topology). Covers key methods, mathematical significance, and real-world applications.
Knot Energy and Optimal Representations
A detailed guide to knot energy and optimal representations. Covers key methods, mathematical significance, and real-world applications.
Knot Floer Homology Invariants
A detailed guide to knot floer homology invariants. Covers key methods, mathematical significance, and real-world applications.
Knot Groups and Fundamental Group of Complement
A detailed guide to knot groups and fundamental group of complement. Covers key methods, mathematical significance, and real-world applications.
Knot Projections and Shadow World
A detailed guide to knot projections and shadow world. Covers key methods, mathematical significance, and real-world applications.
Knot Theory Foundations and Definitions
A detailed guide to knot theory foundations and definitions. Covers key methods, mathematical significance, and real-world applications.
Link Homology Theories and Categorification
A detailed guide to link homology theories and categorification. Covers key methods, mathematical significance, and real-world applications.
Linking Number and Two Component Links (Low Dim Topology)
A detailed guide to linking number and two component links (low dim topology). Covers key methods, mathematical significance, and real-world applications.
Mapping Class Group of a Surface
A detailed guide to mapping class group of a surface. Covers key methods, mathematical significance, and real-world applications.
Monopole Floer Homology and Seiberg Witten
A detailed guide to monopole floer homology and seiberg witten. Covers key methods, mathematical significance, and real-world applications.
Planar Algebras and Subfactor Theory
A detailed guide to planar algebras and subfactor theory. Covers key methods, mathematical significance, and real-world applications.
Prime Decomposition of Three Manifolds
A detailed guide to prime decomposition of three manifolds. Covers key methods, mathematical significance, and real-world applications.
Quantum Invariants from Representation Theory
A detailed guide to quantum invariants from representation theory. Covers key methods, mathematical significance, and real-world applications.
Reidemeister Moves on Knot Diagrams (Low Dim Topology)
A detailed guide to reidemeister moves on knot diagrams (low dim topology). Covers key methods, mathematical significance, and real-world applications.
Ribbon Knots and Slice Knots
Learn about ribbon knots and slice knots — covering Ribbon Knots, Slice Knots, and the role of ribbon knot in this fundamental mathematical topic.
Seifert Fibered Spaces and Classification
A detailed guide to seifert fibered spaces and classification. Covers key methods, mathematical significance, and real-world applications.
Seifert Surfaces for Knots and Links
A detailed guide to seifert surfaces for knots and links. Covers key methods, mathematical significance, and real-world applications.
Skein Modules of Three Manifolds
A detailed guide to skein modules of three manifolds. Covers key methods, mathematical significance, and real-world applications.
Skein Relations and Recursive Computation
A detailed guide to skein relations and recursive computation. Covers key methods, mathematical significance, and real-world applications.
Spatial Graphs and Their Invariants
A detailed guide to spatial graphs and their invariants. Covers key methods, mathematical significance, and real-world applications.
Surface Bundles and Monodromy Representations
A detailed guide to surface bundles and monodromy representations. Covers key methods, mathematical significance, and real-world applications.
Surgery Exact Sequence in Topology
A detailed guide to surgery exact sequence in topology. Covers key methods, mathematical significance, and real-world applications.
Sutured Manifolds and Contact Topology
A detailed guide to sutured manifolds and contact topology. Covers key methods, mathematical significance, and real-world applications.
Three Manifolds and Heegaard Splittings
A detailed guide to three manifolds and heegaard splittings. Covers key methods, mathematical significance, and real-world applications.
Three Sphere Recognition and Poincare Conjecture
A detailed guide to three sphere recognition and poincare conjecture. Covers key methods, mathematical significance, and real-world applications.
Thurston Geometrization Conjecture Proven
A detailed guide to thurston geometrization conjecture proven. Covers key methods, mathematical significance, and real-world applications.
Torus Knots and Their Classification (Low Dim Topology)
A detailed guide to torus knots and their classification (low dim topology). Covers key methods, mathematical significance, and real-world applications.
Tricoloring and Knot Colorability
A detailed guide to tricoloring and knot colorability. Covers key methods, mathematical significance, and real-world applications.
Turaev-Viro Invariants of Three Manifolds
A detailed guide to turaev-viro invariants of three manifolds. Covers key methods, mathematical significance, and real-world applications.
Unknotting Number of a Knot
A detailed guide to unknotting number of a knot. Covers key methods, mathematical significance, and real-world applications.
Virtual Knots and Generalized Invariants
A detailed guide to virtual knots and generalized invariants. Covers key methods, mathematical significance, and real-world applications.
Witten Reshetikhin Turaev Invariants
A detailed guide to witten reshetikhin turaev invariants. Covers key methods, mathematical significance, and real-world applications.