Covering-space actions give quotient coverings: 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. What the colours mean

in mathlib2Upstreamed into Mathlib.fully proved3Proved, and every prerequisite is fully proved too.

graph LR n0["Deck transformations and normal covers"]:::mathlib n1("A lift is determined by one point"):::mathlib n2("Covering-space actions give quotient coverings"):::fully_proved n3["Orbit quotients are normal and have the expected deck group"]:::fully_proved n4["The orbit-quotient fundamental group recovers the acting group"]:::fully_proved n2 --> n3 n2 --> n4 n0 --> n2 n0 --> n3 n3 -.-> n4 n1 -.-> n2 n1 -.-> n3 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/index.html#unique-lifting" "A lift is determined by one point — 1 item · 1 in mathlib" class n2 focus click n2 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#covering-space-action" "Covering-space actions give quotient coverings — 1 item · 1 fully proved" click n3 "../../../../../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" click n4 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#orbit-quotient-fundamental-group" "The orbit-quotient fundamental group recovers the acting group — 1 item · 1 fully proved"