The attaching-sphere pieces generate the intersection 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 proved5Proved, and every prerequisite is fully proved too.

graph LR n0("An open-cover model for attached cells"):::fully_proved n1("The van Kampen cover map is surjective"):::fully_proved n2("The attaching-sphere pieces generate the intersection group"):::fully_proved n3["Attaching higher cells preserves the fundamental group"]:::fully_proved n4["Attaching 2-cells adds the attaching relations"]:::fully_proved n2 -.-> n3 n2 --> n4 n0 -.-> n3 n0 --> n4 n0 --> n2 n1 -.-> n2 click n0 "../../../../roadmap/fundamental-group/van-kampen/index.html#cell-attachment-cover-model" "An open-cover model for attached cells — 1 item · 1 fully proved" click n1 "../../../../roadmap/fundamental-group/van-kampen/index.html#van-kampen-surjective" "The van Kampen cover map is surjective — 1 item · 1 fully proved" class n2 focus click n2 "../../../../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 n3 "../../../../roadmap/fundamental-group/van-kampen/index.html#attach-higher-cells-fundamental-group" "Attaching higher cells preserves the fundamental group — 1 item · 1 fully proved" click n4 "../../../../roadmap/fundamental-group/van-kampen/index.html#attach-two-cells-fundamental-group" "Attaching 2-cells adds the attaching relations — 1 item · 1 fully proved"