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Theorems · Definition · general topology

Matrix.GeneralLinearGroup.parabolicFixedPoint

{K : Type u_1} → [inst : Field K] → [DecidableEq K] → GL (Fin 2) K → OnePoint K

If g is parabolic, this is the unique fixed point of g in OnePoint K.

Defined in
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine
Cited by
3 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isCusp_SL2Z_iff · cited by 3isCusp_SL2Z_iffMatrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff · cited by 3IsParabolic.smul_eq_self_…Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_pow · cited by 1IsParabolic.parabolicFixe…Field · cited by 7404FieldUnits.val · cited by 1966Units.valMatrix.GeneralLinearGroup · cited by 556Matrix.GeneralLinearGroupOnePoint · cited by 126OnePointOnePoint.infty · cited by 102OnePoint.inftyOnePoint.some · cited by 76OnePoint.someGeneralLinearGroup.parabolicF…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.