Khovanov homology

E656685

Khovanov homology is a powerful link invariant in knot theory that lifts the Jones polynomial to a graded homology theory, providing stronger topological information than the polynomial alone.

All labels observed (4)

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Statements (49)

Predicate Object
instanceOf categorification
homology theory
knot invariant
link invariant
basedOn Jones polynomial
categorifies Jones polynomial
coefficientRing finite fields
integers
rational numbers
definedFrom enhanced states of a link diagram
detects more topological information than the Jones polynomial
domain link diagrams
oriented links in S^3
field algebraic topology
knot theory
low-dimensional topology
representation theory
functorialWithRespectTo link cobordisms
generalizedBy Khovanov–Rozansky homology
linked to: HOMFLY-PT homology
hasApplication construction of Rasmussen invariant
study of knot concordance
study of slice genus
hasGrading homological grading
q-grading
hasObjectType bigraded abelian groups
bigraded vector spaces
hasProperty bigraded
functorial
graded
invariant under Reidemeister moves
link invariant up to isomorphism
hasVariant colored Khovanov homology
linked to: Khovanov homology

odd Khovanov homology
linked to: Khovanov homology

reduced Khovanov homology
sl(n) Khovanov–Rozansky homology
linked to: HOMFLY-PT homology
inspired developments in categorification
introducedBy Mikhail Khovanov
isStrongerInvariantThan Jones polynomial
publishedIn Journal of Differential Geometry
relatedTo Heegaard Floer homology
linked to: Floer theory

categorified quantum sl(2)
knot Floer homology
quantum groups
usedToDefine s-invariant of a knot
usesConstruction Frobenius algebra
chain complex
cube of resolutions
yearOfIntroduction 1999
yields Jones polynomial as graded Euler characteristic

How these facts were elicited

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Jones polynomial categorifiedBy Khovanov homology
Khovanov homology hasVariant odd Khovanov homology
linked to: Khovanov homology
Khovanov homology hasVariant colored Khovanov homology
linked to: Khovanov homology
HOMFLY-PT homology relatedTo Khovanov homology
HOMFLY-PT homology generalizes Khovanov-Rozansky sl(N) homology
linked to: Khovanov homology