Theorems · Definition · algebraic topology

IsAddQuotientCoveringMap.fundamentalGroupEquiv

{E : Type u_1} →
  {X : Type u_2} →
    [inst : TopologicalSpace E] →
      [inst_1 : TopologicalSpace X] →
        {p : E → X} →
          {G : Type u_4} →
            [inst_2 : AddGroup G] →
              [inst_3 : AddAction G E] →
                IsAddQuotientCoveringMap p G →
                  {x : X} → ↑(p ⁻¹' {x}) → [SimplyConnectedSpace E] → FundamentalGroup X x ≃* (Multiplicative G)ᵐᵒᵖ

The fundamental group of the base of simply-connected covering map is contravariantly equivalent to the group of the covering map.

Defined in

Mathlib.Topology.Homotopy.Lifting

Cited by

0 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceAddGroupAddActionSimplyConnectedSpace