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- Dehn_function abstract "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. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The Dehn function of a finitely presented group is also closely connected with non-deterministic algorithmic complexity of the word problem in groups. In particular, a finitely presented group has solvable word problem if and only if the Dehn function for a finite presentation of this group is recursive (see Theorem 2.1 in ). The notion of a Dehn function is motivated by isoperimetric problems in geometry, such as the classic isoperimetric inequality for the Euclidean plane and, more generally, the notion of a filling area function that estimates the area of a minimal surface in a Riemannian manifold in terms of the length of the boundary curve of that surface.".
- Dehn_function wikiPageExternalLink books?id=VB_f6xnmvikC&pg=PA29&dq=The+geometry+of+the+word+problem.+Invitations+to+geometry+and+topology,&ei=KWcMSZrFHovCMqiWzLME&client=firefox-a.
- Dehn_function wikiPageExternalLink 14.
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- Dehn_function wikiPageExternalLink bfs.pdf.
- Dehn_function wikiPageID "20017026".
- Dehn_function wikiPageLength "28711".
- Dehn_function wikiPageOutDegree "90".
- Dehn_function wikiPageRevisionID "666382681".
- Dehn_function wikiPageWikiLink American_Institute_of_Mathematics.
- Dehn_function wikiPageWikiLink Automatic_group.
- Dehn_function wikiPageWikiLink Baumslag-Solitar_group.
- Dehn_function wikiPageWikiLink Baumslag–Solitar_group.
- Dehn_function wikiPageWikiLink CAT(0)_space.
- Dehn_function wikiPageWikiLink Category:Combinatorics_on_words.
- Dehn_function wikiPageWikiLink Category:Geometric_group_theory.
- Dehn_function wikiPageWikiLink Category:Geometric_topology.
- Dehn_function wikiPageWikiLink Combable_group.
- Dehn_function wikiPageWikiLink Conjugate_closure.
- Dehn_function wikiPageWikiLink DSPACE.
- Dehn_function wikiPageWikiLink Deterministic_algorithm.
- Dehn_function wikiPageWikiLink Eliyahu_Rips.
- Dehn_function wikiPageWikiLink Equivalence_relation.
- Dehn_function wikiPageWikiLink Filling_length_function.
- Dehn_function wikiPageWikiLink Finitely_presented_group.
- Dehn_function wikiPageWikiLink Free_abelian_group.
- Dehn_function wikiPageWikiLink Free_group.
- Dehn_function wikiPageWikiLink Fundamental_group.
- Dehn_function wikiPageWikiLink Geometric_group_theory.
- Dehn_function wikiPageWikiLink Group_automorphism.
- Dehn_function wikiPageWikiLink Group_isomorphism.
- Dehn_function wikiPageWikiLink Hadamard_space.
- Dehn_function wikiPageWikiLink Heisenberg_group.
- Dehn_function wikiPageWikiLink Higmans_embedding_theorem.
- Dehn_function wikiPageWikiLink Homotopy.
- Dehn_function wikiPageWikiLink Hyperbolic_group.
- Dehn_function wikiPageWikiLink Identity_element.
- Dehn_function wikiPageWikiLink Isodiametric_function.
- Dehn_function wikiPageWikiLink Isoperimetric_inequality.
- Dehn_function wikiPageWikiLink Mapping_class_group.
- Dehn_function wikiPageWikiLink Max_Dehn.
- Dehn_function wikiPageWikiLink Mikhail_Gromov_(mathematician).
- Dehn_function wikiPageWikiLink Mikhail_Leonidovich_Gromov.
- Dehn_function wikiPageWikiLink Minimal_surface.
- Dehn_function wikiPageWikiLink Nilpotent_group.
- Dehn_function wikiPageWikiLink Non-deterministic_algorithm.
- Dehn_function wikiPageWikiLink Nondeterministic_algorithm.
- Dehn_function wikiPageWikiLink Normal_closure_(group_theory).
- Dehn_function wikiPageWikiLink Null-homotopic.
- Dehn_function wikiPageWikiLink Oxford_University_Press.
- Dehn_function wikiPageWikiLink Presentation_complex.
- Dehn_function wikiPageWikiLink Presentation_of_a_group.
- Dehn_function wikiPageWikiLink Quasi-isometry.
- Dehn_function wikiPageWikiLink Recursion.
- Dehn_function wikiPageWikiLink Relatively_hyperbolic_group.
- Dehn_function wikiPageWikiLink Riemannian_manifold.
- Dehn_function wikiPageWikiLink Rostislav_Grigorchuk.
- Dehn_function wikiPageWikiLink Sectional_curvature.
- Dehn_function wikiPageWikiLink Simply_connected_space.
- Dehn_function wikiPageWikiLink Small_cancellation_theory.
- Dehn_function wikiPageWikiLink Space_complexity.
- Dehn_function wikiPageWikiLink Thompson_groups.
- Dehn_function wikiPageWikiLink Turing_machine.
- Dehn_function wikiPageWikiLink Ultralimit.
- Dehn_function wikiPageWikiLink Van_Kampen_diagram.
- Dehn_function wikiPageWikiLink Word-hyperbolic_group.
- Dehn_function wikiPageWikiLink Word_problem_for_groups.
- Dehn_function wikiPageWikiLinkText "Dehn function".
- Dehn_function wikiPageWikiLinkText "isoperimetric function".
- Dehn_function wikiPageWikiLinkText "isoperimetric inequality".
- Dehn_function hasPhotoCollection Dehn_function.
- Dehn_function wikiPageUsesTemplate Template:Reflist.
- Dehn_function subject Category:Combinatorics_on_words.
- Dehn_function subject Category:Geometric_group_theory.
- Dehn_function subject Category:Geometric_topology.
- Dehn_function hypernym Function.
- Dehn_function type ProgrammingLanguage.
- Dehn_function type Combinatoric.
- Dehn_function comment "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. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group.".
- Dehn_function label "Dehn function".
- Dehn_function sameAs m.04y6ft2.
- Dehn_function sameAs Функция_Дена.
- Dehn_function sameAs Q4493444.
- Dehn_function sameAs Q4493444.
- Dehn_function wasDerivedFrom Dehn_function?oldid=666382681.
- Dehn_function isPrimaryTopicOf Dehn_function.