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Diff — Geometric group theory

Revision #2286 → #2953 · back to history

modifiedGeometric group theory797ca6d202a9
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noteThe field itself is not formalized, but its central object—finitely generated groups—is captured by the `Group.FG` class.The field itself is not formalized, but its central object—finitely generated groups—is captured by the `Group.FG` typeclass.
modifiedCayley graph and word metric9cbd480ce7f3
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note`SimpleGraph.mulCayley` directly defines the Cayley graph from a generating set, though the word metric is not separately packaged.`SimpleGraph.mulCayley s` defines the Cayley graph from a generating set, though the word metric is not separately packaged.
modifiedGromov's polynomial growth theorema65f1757253b
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noteNo formalization of group growth or Gromov's theorem exists in Mathlib.No formalization of group growth or Gromov's polynomial growth theorem exists in Mathlib.
modifiedStallings' ends theoremb5d6bcd95dfb
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noteNeither the ends of groups nor Stallings' theorem is formalized.Neither the ends of groups nor Stallings' theorem is formalized in Mathlib.
modifiedMostow rigidity theoreme09a5cb295ea
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noteMostow rigidity is not present in Mathlib (loogle returns zero hits for 'Mostow').Mostow rigidity is not present in Mathlib.
modifiedDehn function / isoperimetric function7214b9441a2e
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noteDehn functions of finitely presented groups are not formalized in Mathlib (loogle returns zero 'Dehn' hits).Dehn functions of finitely presented groups are not formalized in Mathlib.
modifiedKazhdan's property (T)f7c76292a9d0
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noteKazhdan's property (T) for discrete groups is not formalized in Mathlib (loogle returns zero 'Kazhdan' hits).Kazhdan's property (T) for discrete groups is not formalized in Mathlib.
modifiedAmenable groups53e3668e776c
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noteMathlib has Følner-filter amenability (`IsFoelner.amenable`) but no standalone definition of an amenable group as a class.Mathlib has the Følner-filter amenability theorem (`IsFoelner.amenable`) but no standalone `Amenable` group typeclass.
modifiedFree productsec8063f3611f
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note`Monoid.CoprodI` is the free product (coproduct) of a family of groups, with binary `Monoid.Coprod` as a special case.`Monoid.CoprodI` is the free product (coproduct) of a family of groups.
modifiedOuter automorphism groups Out(Fn)0d03171d0742
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noteMathlib has `MulAut` and `FreeGroup` but no `OuterAut`/Out(Fn) construction (loogle returns zero 'OuterAut' hits).Mathlib has `MulAut` and `FreeGroup` but no `OuterAut`/Out(Fn) construction.
modifiedMapping class groups19c36facf34d
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noteMapping class groups of surfaces are not formalized.Mapping class groups of surfaces are not formalized in Mathlib.
modifiedGeneral Artin groups694a3995d4e6
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noteArtin groups are not defined; Mathlib only mentions the 'Artin–Tits relation' in a comment within the Coxeter files.Artin groups are not defined; Mathlib only mentions the 'Artin–Tits relation' in comments in the Coxeter files.
modifiedFuchsian and Kleinian groups7fbc36da0d22
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noteNeither Fuchsian nor Kleinian groups are formalized.Neither Fuchsian nor Kleinian groups are formalized in Mathlib.
modifiedBaumslag–Solitar groupsf3939a5a2244
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noteBaumslag–Solitar groups are HNN extensions of ℤ; Mathlib has the general `HNNExtension` construction but not these specific groups (loogle returns zero 'BaumslagSolitar' hits).Baumslag–Solitar groups are HNN extensions of ℤ; Mathlib has the general `HNNExtension` construction but not these specific groups.
modifiedGrigorchuk group8f80adcf2e64
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noteThe Grigorchuk group is not formalized in Mathlib (loogle returns zero 'Grigorchuk' hits).The Grigorchuk group is not formalized in Mathlib.
addedSmall cancellation theory9d25437ff190
addedvan Kampen diagramsc0592fa66305
addedBaum–Connes conjecture2290acc2a6b9
addedNovikov conjectureeb0ef012cb86
addedBurnside problem226d7c07edc2
addedGrowth rate of a finitely generated groupc14bf79ecf3e
addedNumber of ends of a group99124bc7c4fb
addedAsymptotic dimension31feb705a4be