Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
simplicial volume
|
| gptkbp:appliesTo |
oriented closed manifolds
|
| gptkbp:citation |
gptkb:Gromov,_M._(1982)._Volume_and_bounded_cohomology._Publications_Mathématiques_de_l'IHÉS.
|
| gptkbp:defines |
infimum of the sum of absolute values of coefficients over all singular chains representing the fundamental class
|
| gptkbp:field |
gptkb:geometry
gptkb:topology |
| https://www.w3.org/2000/01/rdf-schema#label |
Gromov norm
|
| gptkbp:introduced |
gptkb:Mikhail_Gromov
|
| gptkbp:property |
vanishes for manifolds admitting a self-map of degree greater than one
nonzero for hyperbolic manifolds proportional to hyperbolic volume for hyperbolic manifolds |
| gptkbp:relatedTo |
homology
fundamental class simplicial chain |
| gptkbp:usedIn |
3-manifold theory
geometric topology |
| gptkbp:bfsParent |
gptkb:Mikhail_Gromov
|
| gptkbp:bfsLayer |
5
|