Higher spheres are simply connected: 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("Higher spheres are simply connected"):::fully_proved n2("Borsuk–Ulam for the two-sphere"):::fully_proved n3("Euclidean two-space is distinguished by dimension"):::fully_proved n4["Attaching higher cells preserves the fundamental group"]:::fully_proved n0 --> n1 n1 --> n2 n1 --> n3 n1 -.-> 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" class n1 focus click n1 "../../../../roadmap/fundamental-group/basic-constructions/index.html#sphere-simply-connected" "Higher spheres are simply connected — 1 item · 1 fully proved" click n2 "../../../../roadmap/fundamental-group/basic-constructions/index.html#borsuk-ulam-sphere" "Borsuk–Ulam for the two-sphere — 1 item · 1 fully proved" click n3 "../../../../roadmap/fundamental-group/basic-constructions/index.html#euclidean-two-not-homeomorphic" "Euclidean two-space is distinguished by dimension — 1 item · 1 fully proved" click n4 "../../../../roadmap/fundamental-group/van-kampen/index.html#attach-higher-cells-fundamental-group" "Attaching higher cells preserves the fundamental group — 1 item · 1 fully proved"