A deck transformation is determined by one lifted point: 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 mathlib2Upstreamed into Mathlib.fully proved5Proved, and every prerequisite is fully proved too.
graph LR
n0["Pointed connected covering spaces"]:::fully_proved
n1["Deck transformations and normal covers"]:::mathlib
n2("A lift is determined by one point"):::mathlib
n3("Equal image subgroups characterize pointed cover isomorphism"):::fully_proved
n4("A deck transformation is determined by one lifted point"):::fully_proved
n5["The normalizer acts by deck transformations"]:::fully_proved
n6("The normalizer map is surjective with kernel the covering subgroup"):::fully_proved
n0 --> n4
n0 --> n5
n0 --> n3
n4 -.-> n5
n4 -.-> n6
n1 --> n4
n1 --> n5
n5 --> n6
n3 -.-> n4
n2 -.-> n4
n2 -.-> n3
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/deck-transformations/index.html#deck-transformation-group" "Deck transformations and normal covers — 1 item · 1 in mathlib"
click n2 "../../../../../roadmap/fundamental-group/covering-spaces/index.html#unique-lifting" "A lift is determined by one point — 1 item · 1 in mathlib"
click n3 "../../../../../roadmap/fundamental-group/covering-spaces/index.html#pointed-cover-rigidity" "Equal image subgroups characterize pointed cover isomorphism — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../../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 n5 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#normalizer-to-deck" "The normalizer acts by deck transformations — 1 item · 1 fully proved"
click n6 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#normalizer-to-deck-exactness" "The normalizer map is surjective with kernel the covering subgroup — 1 item · 1 fully proved"