Reduced homology of spheres: 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 proved6Proved, and every prerequisite is fully proved too.

graph LR n0["Reduced singular homology"]:::fully_proved n1("The reduced homology of spheres satisfies the suspension recurrence"):::fully_proved n2("Reduced homology of the zero-sphere"):::fully_proved n3("Reduced homology of spheres"):::fully_proved n4("Local homology of positive-dimensional Euclidean space"):::fully_proved n5("The boundary sphere is not a retract of the disk"):::fully_proved n3 -.-> n4 n3 -.-> n5 n1 -.-> n3 n2 -.-> n3 n0 --> n3 n0 --> n1 n0 --> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#reduced-singular-homology" "Reduced singular homology — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#sphere-reduced-homology-recurrence" "The reduced homology of spheres satisfies the suspension recurrence — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#zero-sphere-reduced-homology" "Reduced homology of the zero-sphere — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#sphere-reduced-homology" "Reduced homology of spheres — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/local-homology-and-dimension/index.html#punctured-euclidean-local-homology" "Local homology of positive-dimensional Euclidean space — 1 item · 1 fully proved" click n5 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#disk-boundary-no-retraction" "The boundary sphere is not a retract of the disk — 1 item · 1 fully proved"