nLab knot theory - contents

knot theory

knot, link

• isotopy

• knot complement

• knot diagrams, chord diagram

• Reidemeister move

Examples/classes:

• trefoil knot

• torus knot

• singular knot

• hyperbolic knot

• Borromean link

• Whitehead link

• Hopf link

Types

• prime knot

• mutant knot

knot invariants

• crossing number

• bridge number

• unknotting number

• colorability

• knot group

• knot genus?

• polynomial knot invariants

  (observables of non-perturbative Chern-Simons theory)

  • Jones polynomial

  • HOMFLY polynomial

  • Alexander polynomial

  • Reshetikhin-Turaev invariants

• Vassiliev knot invariants

  (observables of pertrubative Chern-Simons theory)

• Khovanov homology

• Kauffman bracket?

link invariants

• Milnor mu-bar invariants

• linking number

Related concepts:

• Vassiliev skein relation

• Seifert surface

• virtual knot theory

• Dehn surgery, Kirby calculus

• volume conjecture

• arithmetic topology

category: knot theory