Pointed connected covering spaces: 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 proved8Proved, 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("A deck transformation is determined by one lifted point"):::fully_proved
n3["The normalizer acts by deck transformations"]:::fully_proved
n4["The deck group is the normalizer quotient"]:::fully_proved
n5["Pointed connected covers are classified by subgroups"]:::fully_proved
n6("A simply-connected cover maps uniquely to every pointed connected cover"):::fully_proved
n7["Connected covers are classified by conjugacy classes"]:::fully_proved
n0 --> n4
n0 --> n2
n0 --> n3
n0 --> n5
n0 --> n1
n0 --> n6
n0 --> n7
n2 -.-> n3
n5 -.-> n7
n1 -.-> n2
n1 -.-> n5
class n0 focus
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/deck-transformations/index.html#deck-realization" "A deck transformation is determined by one lifted point — 1 item · 1 fully proved"
click n3 "../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#normalizer-to-deck" "The normalizer acts by deck transformations — 1 item · 1 fully proved"
click n4 "../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#deck-group-calculation" "The deck group is the normalizer quotient — 1 item · 1 fully proved"
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#universal-cover-initial" "A simply-connected cover maps uniquely to every pointed connected cover — 1 item · 1 fully proved"
click n7 "../../../../roadmap/fundamental-group/covering-spaces/index.html#unpointed-cover-classification" "Connected covers are classified by conjugacy classes — 1 item · 1 fully proved"