The reduced homology of spheres satisfies the suspension recurrence: 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. fully proved7Proved, and every prerequisite is fully proved too.
graph LR
n0["Reduced singular homology"]:::fully_proved
n1("Reduced homology of a contractible space vanishes"):::fully_proved
n2["Stereographic models for hemispheres and the equator"]:::fully_proved
n3("The reduced neighborhood-retract Mayer–Vietoris sequence"):::fully_proved
n4["The hemispheres have compatible neighborhood deformation retractions"]:::fully_proved
n5("The reduced homology of spheres satisfies the suspension recurrence"):::fully_proved
n6("Reduced homology of spheres"):::fully_proved
n1 -.-> n5
n3 -.-> n5
n4 -.-> n5
n2 --> n4
n2 -.-> n5
n5 -.-> n6
n0 --> n1
n0 --> n6
n0 --> n5
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#contractible-space-reduced-homology" "Reduced homology of a contractible space vanishes — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#sphere-hemisphere-stereographic-models" "Stereographic models for hemispheres and the equator — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#reduced-neighborhood-mayer-vietoris" "The reduced neighborhood-retract Mayer–Vietoris sequence — 1 item · 1 fully proved"
click n4 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#sphere-hemisphere-neighborhood-cover" "The hemispheres have compatible neighborhood deformation retractions — 1 item · 1 fully proved"
class n5 focus
click n5 "../../../../../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 n6 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#sphere-reduced-homology" "Reduced homology of spheres — 1 item · 1 fully proved"