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)

How this entity was disambiguated

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