The deck group is the normalizer quotient: 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0["Pointed connected covering spaces"]:::fully_proved n1["The fundamental group acts on a covering fiber"]:::mathlib n2["Deck transformations and normal covers"]:::mathlib n3("The normalizer map is surjective with kernel the covering subgroup"):::fully_proved n4["The deck group is the normalizer quotient"]:::fully_proved n5["The orbit-quotient fundamental group recovers the acting group"]:::fully_proved n0 --> n4 n4 -.-> n5 n2 --> n4 n3 -.-> n4 n1 -.-> n4 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#monodromy-action" "The fundamental group acts on a covering fiber — 1 item · 1 in mathlib" click n2 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#deck-transformation-group" "Deck transformations and normal covers — 1 item · 1 in mathlib" click n3 "../../../../../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" class n4 focus 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-fundamental-group" "The orbit-quotient fundamental group recovers the acting group — 1 item · 1 fully proved"