Deck transformations and normal covers: 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 proved5Proved, and every prerequisite is fully proved too.
graph LR
n0["Deck transformations and normal covers"]:::mathlib
n1("Covering-space actions give quotient coverings"):::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["Orbit quotients are normal and have the expected deck group"]:::fully_proved
n1 --> n5
n2 -.-> n3
n0 --> n1
n0 --> n4
n0 --> n2
n0 --> n3
n0 --> n5
class n0 focus
click n0 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#deck-transformation-group" "Deck transformations and normal covers — 1 item · 1 in mathlib"
click n1 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#covering-space-action" "Covering-space actions give quotient coverings — 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/deck-transformations/index.html#orbit-quotient-deck-group" "Orbit quotients are normal and have the expected deck group — 1 item · 1 fully proved"