The van Kampen cover map is surjective: 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("A loop splits across an open cover"):::fully_proved n1["The group presentation associated to an open cover"]:::fully_proved n2("The van Kampen cover map is surjective"):::fully_proved n3("The attaching-sphere pieces generate the intersection group"):::fully_proved n4["Van Kampen's quotient isomorphism"]:::fully_proved n0 -.-> n2 n1 --> n2 n2 -.-> n3 n2 -.-> n4 click n0 "../../../../roadmap/fundamental-group/basic-constructions/index.html#loop-in-open-cover" "A loop splits across an open cover — 1 item · 1 fully proved" click n1 "../../../../roadmap/fundamental-group/van-kampen/index.html#cover-group-presentation" "The group presentation associated to an open cover — 1 item · 1 fully proved" class n2 focus click n2 "../../../../roadmap/fundamental-group/van-kampen/index.html#van-kampen-surjective" "The van Kampen cover map is surjective — 1 item · 1 fully proved" click n3 "../../../../roadmap/fundamental-group/van-kampen/index.html#attaching-spheres-generate-intersection" "The attaching-sphere pieces generate the intersection group — 1 item · 1 fully proved" click n4 "../../../../roadmap/fundamental-group/van-kampen/index.html#van-kampen-quotient" "Van Kampen's quotient isomorphism — 1 item · 1 fully proved"