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Dehn function

In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the generators representing the identity element of the group) in terms of the length of that relation (see pp.…

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Dehn function

Nodes54
Edges53
Triples92
Avg. degree1.96
Density0.037037
Components1

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Dehn function

Top relations

related to Known results · 39
Dehn function → Although, Aut, Automatic, Birget, Bridson, CAT, Dehn, Exponential, Fk, For, For SL, Gromov's, Handel, Hatcher, Higman's, If, In, Isoperimetric, Leuzinger, Lie
related to Generalizations · 17
Dehn function → Asymptotic, Compared, Dehn, For, Grigorchuk, Gromov, Here, In, Ivanov, Kampen, Lie, More, One, Osin, The, There, Thus
related to history · 16
Dehn function → Birget, Dehn, Dehn's, Gromov, Gromov's, Hyperbolic, In, Martin Greendlinger, Max Dehn, One, Riemannian, Rips, Sapir, The, This, Turing
related to Basic properties · 13
Dehn function → Area, As, Consequently, Dehn, Exp, For, However, If, In, Knowing, More, The, There
related to Dehn function · 3
Dehn function → Dehn, Equivalently, Then
related to Growth types of functions · 3
Dehn function → Because, Dehn, For
is a · 1
Dehn function → quasi-isometry invariant of a finitely presented group

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Important terminology

dehn function group isoperimetric finitely presented groups word presentation functions finite problem equivalent inequality length area quadratic filling terms satisfies

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dehn functionis aquasi-isometry invariant of a finitely presented group0.90text
Dehn functionrelated to Basic propertiesIf0.60section
Dehn functionrelated to Basic propertiesIn0.60section
Dehn functionrelated to Basic propertiesConsequently0.60section
Dehn functionrelated to Basic propertiesDehn0.60section
Dehn functionrelated to Basic propertiesMore0.60section
Dehn functionrelated to Basic propertiesFor0.60section
Dehn functionrelated to Basic propertiesThere0.60section
Dehn functionrelated to Basic propertiesThe0.60section
Dehn functionrelated to Basic propertiesKnowing0.60section
Dehn functionrelated to Basic propertiesArea0.60section
Dehn functionrelated to Basic propertiesAs0.60section

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