Pointed connected covers are classified by subgroups: 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. fully proved7Proved, and every prerequisite is fully proved too.
graph LR
n0["Pointed connected covering spaces"]:::fully_proved
n1("Equal image subgroups characterize pointed cover isomorphism"):::fully_proved
n2["Semilocally simply-connected spaces"]:::fully_proved
n3["The covering space associated to a subgroup"]:::fully_proved
n4("The subgroup cover realizes the chosen subgroup"):::fully_proved
n5["Pointed connected covers are classified by subgroups"]:::fully_proved
n6["Connected covers are classified by conjugacy classes"]:::fully_proved
n0 --> n5
n0 --> n1
n0 --> n6
n5 -.-> n6
n1 -.-> n5
n4 -.-> n5
n3 -.-> n5
n3 --> n4
n2 --> n5
n2 --> n6
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#pointed-cover-rigidity" "Equal image subgroups characterize pointed cover isomorphism — 1 item · 1 fully proved"
click n2 "../../../../roadmap/fundamental-group/covering-spaces/universal-cover/index.html#semilocally-simply-connected" "Semilocally simply-connected spaces — 1 item · 1 fully proved"
click n3 "../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-space" "The covering space associated to a subgroup — 1 item · 1 fully proved"
click n4 "../../../../roadmap/fundamental-group/covering-spaces/index.html#subgroup-cover-image" "The subgroup cover realizes the chosen subgroup — 1 item · 1 fully proved"
class n5 focus
click n5 "../../../../roadmap/fundamental-group/covering-spaces/index.html#pointed-cover-classification" "Pointed connected covers are classified by subgroups — 1 item · 1 fully proved"
click n6 "../../../../roadmap/fundamental-group/covering-spaces/index.html#unpointed-cover-classification" "Connected covers are classified by conjugacy classes — 1 item · 1 fully proved"