Theorems · Definition · algebraic topology
IsCoveringMap.monodromyPerm
{E : Type u_1} →
{X : Type u_2} →
[inst : TopologicalSpace E] →
[inst_1 : TopologicalSpace X] →
{p : E → X} → IsCoveringMap p → (x : X) → FundamentalGroup X x →* Equiv.Perm ↑(p ⁻¹' {x})The monodromy action of the fundamental group at x on the fiber over x.
- Defined in
- Mathlib.Topology.Homotopy.Lifting
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement and proof · cited by 7,166
- Set.preimagestatement and proof · cited by 4,946
- MonoidHomstatement · cited by 3,629
- Equiv.Permstatement · cited by 1,375
- IsCoveringMapstatement and proof · cited by 68
- FundamentalGroupoidstatement · cited by 60
- FundamentalGroupstatement and proof · cited by 30
- MulAction.toPermHomproof · cited by 16
Cited by11
Results whose statement or proof uses this declaration.
- IsQuotientCoveringMap.monodromyPerm_injectivestatement and proof · cited by 2
- IsQuotientCoveringMap.ker_monodromyPermstatement and proof · cited by 2
- IsQuotientCoveringMap.ker_fundamentalGroupToMulOppositestatement · cited by 2
- IsQuotientCoveringMap.commute_monodromyPerm_toPermFiberstatement · cited by 1
- IsQuotientCoveringMap.fundamentalGroupToMulOpposite_injectiveproof · cited by 1
- IsAddQuotientCoveringMap.ker_fundamentalGroupToMulOppositestatement · cited by 0
- IsAddQuotientCoveringMap.ker_monodromyPermstatement · cited by 0
- IsCoveringMap.monodromyPerm.congr_simpstatement and proof · cited by 0
- IsAddQuotientCoveringMap.monodromyPerm_injectivestatement · cited by 0
- IsAddQuotientCoveringMap.commute_monodromyPerm_toPermFiberstatement · cited by 0
- IsCoveringMap.coe_monodromyPermstatement · cited by 0