The orbit-quotient fundamental group recovers the acting group: 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

fully proved4Proved, and every prerequisite is fully proved too.

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