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Diff — Geometric group theory

Revision #2953 → #3448 · 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` typeclass.The field itself is not formalized, but its central object—finitely generated groups—is captured by the `Group.FG` typeclass (verified).
modifiedCayley graph and word metric9cbd480ce7f3
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note`SimpleGraph.mulCayley s` defines the Cayley graph from a generating set, though the word metric is not separately packaged.`SimpleGraph.mulCayley s` (verified) defines the Cayley graph from a generating set; the word metric is not separately packaged.
modifiedGroup presentation2846f9441d80
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note`PresentedGroup rels` constructs the group with the given generators and relations as a quotient of the free group.`PresentedGroup rels` (verified) constructs the group with the given generators and relations as a quotient of the free group.
modifiedHyperbolic groupa9cb61ae7102
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noteMathlib's only 'hyperbolic' references are to hyperbolic functions/geometry and `Matrix.IsHyperbolic`, not Gromov-hyperbolic groups.Mathlib's only 'hyperbolic' references are to hyperbolic functions/geometry and `Matrix.GeneralLinearGroup.IsHyperbolic`, not Gromov-hyperbolic groups.
modifiedBass–Serre theory5519795f7242
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noteThe Bass–Serre building blocks—amalgamated free products (`Monoid.PushoutI`) and HNN extensions (`HNNExtension`)—are formalized, but the full graph-of-groups/tree-action framework is not.The Bass–Serre building blocks—amalgamated free products (`Monoid.PushoutI`, verified) and HNN extensions (`HNNExtension`, verified)—are formalized, but the full graph-of-groups/tree-action framework is not.
modifiedAmenable groups53e3668e776c
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noteMathlib has the Følner-filter amenability theorem (`IsFoelner.amenable`) but no standalone `Amenable` group typeclass.Mathlib has the Følner-filter amenability theorem (`IsFoelner.amenable`, verified) but no standalone `Amenable` group typeclass.
modifiedInfinite cyclic group Zc2ccd70ca542
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noteThe infinite cyclic group is exactly ℤ, whose additive group structure is `Int.instAddCommGroup`.The infinite cyclic group is exactly ℤ, whose additive group structure `Int.instAddCommGroup` is verified in Mathlib.
modifiedFree groups960d5ebcf528
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note`FreeGroup α` is the free group on a generating type α.`FreeGroup α` (verified) is the free group on a generating type α.
modifiedFree productsec8063f3611f
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note`Monoid.CoprodI` is the free product (coproduct) of a family of groups.`Monoid.CoprodI` (verified) is the free product (coproduct) of a family of groups.
modifiedSymmetric groups344da8d8a6ea
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note`Equiv.Perm α` is the symmetric group of permutations of α.`Equiv.Perm α` (verified) is the symmetric group of permutations of α.
modifiedCoxeter groupseb46761186f6
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note`CoxeterSystem` and the `IsCoxeterGroup` class formalize Coxeter groups.`CoxeterSystem` (verified) together with `IsCoxeterGroup` (verified) formalize Coxeter groups.
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.Baumslag–Solitar groups are HNN extensions of ℤ; Mathlib has the general `HNNExtension` construction (verified) but not these specific groups.
modifiedFundamental groups of graphs of groups2483e92e4704
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noteThe Bass–Serre building blocks—amalgamated products (`Monoid.PushoutI`) and HNN extensions—exist, but graph-of-groups fundamental groups are not formalized.The Bass–Serre building blocks—amalgamated products (`Monoid.PushoutI`, verified) and HNN extensions—exist, but graph-of-groups fundamental groups are not formalized.
modifiedBurnside problem226d7c07edc2
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noteThe Burnside problem on periodic finitely generated groups is not formalized in Mathlib.The Burnside problem on periodic finitely generated groups is not formalized in Mathlib (only the group exponent machinery `Monoid.exponent` exists).
addedFinitely presented group2de41d05f256
addedCannon's conjecture9a8234f83da0
addedPoisson boundarycf8315c1e46d
addedGroup actions on R-trees (Rips machine)255bc2f3583d
addedSubgroup growth69b5f84ed818