The normalizer map is surjective with kernel the covering subgroup: 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 proved5Proved, and every prerequisite is fully proved too.

graph LR n0("The induced subgroup consists of loops with closed lifts"):::fully_proved n1("A deck transformation is determined by one lifted point"):::fully_proved n2["The normalizer acts by deck transformations"]:::fully_proved n3("The normalizer map is surjective with kernel the covering subgroup"):::fully_proved n4["The deck group is the normalizer quotient"]:::fully_proved n0 -.-> n3 n1 -.-> n2 n1 -.-> n3 n2 --> n3 n3 -.-> n4 click n0 "../../../../../roadmap/fundamental-group/covering-spaces/index.html#closed-lift-image" "The induced subgroup consists of loops with closed lifts — 1 item · 1 fully proved" click n1 "../../../../../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 n2 "../../../../../roadmap/fundamental-group/covering-spaces/deck-transformations/index.html#normalizer-to-deck" "The normalizer acts by deck transformations — 1 item · 1 fully proved" class n3 focus 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" 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"