The fundamental group acts on a covering fiber: 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 mathlib1Upstreamed into Mathlib.fully proved5Proved, and every prerequisite is fully proved too.

graph LR n0["The fundamental group acts on a covering fiber"]:::mathlib n1("The induced subgroup consists of loops with closed lifts"):::fully_proved n2("Changing the lifted basepoint conjugates the image subgroup"):::fully_proved n3["The normalizer acts by deck transformations"]:::fully_proved n4["The deck group is the normalizer quotient"]:::fully_proved n5["Sheets are cosets of the induced subgroup"]:::fully_proved n1 -.-> n2 n1 -.-> n5 n2 -.-> n3 n0 --> n1 n0 -.-> n2 n0 -.-> n4 n0 --> n3 n0 -.-> n5 class n0 focus click n0 "../../../../roadmap/fundamental-group/covering-spaces/index.html#monodromy-action" "The fundamental group acts on a covering fiber — 1 item · 1 in mathlib" click n1 "../../../../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 n2 "../../../../roadmap/fundamental-group/covering-spaces/index.html#cover-basepoint-conjugacy" "Changing the lifted basepoint conjugates the image subgroup — 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/index.html#sheet-index" "Sheets are cosets of the induced subgroup — 1 item · 1 fully proved"