Equal image subgroups characterize pointed cover isomorphism: local context
Project map · Chapter map · Full theorem DAG · Open textbook statement
This local map shows one dependency hop in either direction. The highlighted item is the current focus. in mathlib1Upstreamed into Mathlib.fully proved6Proved, and every prerequisite is fully proved too.
graph LR
n0["Pointed connected covering spaces"]:::fully_proved
n1("A lift is determined by one point"):::mathlib
n2("A map lifts exactly when its fundamental group lands in the covering subgroup"):::fully_proved
n3("Local path-connectedness ascends along a covering"):::fully_proved
n4("Equal image subgroups characterize pointed cover isomorphism"):::fully_proved
n5("A deck transformation is determined by one lifted point"):::fully_proved
n6["Pointed connected covers are classified by subgroups"]:::fully_proved
n0 --> n5
n0 --> n6
n0 --> n4
n2 -.-> n4
n3 -.-> n4
n4 -.-> n5
n4 -.-> n6
n1 -.-> n5
n1 -.-> n4
click n0 "../../../../roadmap/fundamental-group/covering-spaces/index.html#based-connected-cover" "Pointed connected covering spaces — 1 item · 1 fully proved"
click n1 "../../../../roadmap/fundamental-group/covering-spaces/index.html#unique-lifting" "A lift is determined by one point — 1 item · 1 in mathlib"
click n2 "../../../../roadmap/fundamental-group/covering-spaces/index.html#lifting-criterion" "A map lifts exactly when its fundamental group lands in the covering subgroup — 1 item · 1 fully proved"
click n3 "../../../../roadmap/fundamental-group/covering-spaces/index.html#locally-path-connected-total-space" "Local path-connectedness ascends along a covering — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../roadmap/fundamental-group/covering-spaces/index.html#pointed-cover-rigidity" "Equal image subgroups characterize pointed cover isomorphism — 1 item · 1 fully proved"
click n5 "../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#deck-realization" "A deck transformation is determined by one lifted point — 1 item · 1 fully proved"
click n6 "../../../../roadmap/fundamental-group/covering-spaces/index.html#pointed-cover-classification" "Pointed connected covers are classified by subgroups — 1 item · 1 fully proved"