The hemispheres have compatible neighborhood deformation retractions: 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 proved6Proved, and every prerequisite is fully proved too.
graph LR
n0["Stereographic models for hemispheres and the equator"]:::fully_proved
n1("The ordinary neighborhood-retract Mayer–Vietoris sequence"):::fully_proved
n2["A sphere strongly deformation retracts from punctured Euclidean space"]:::fully_proved
n3["A closed ball strongly deformation retracts from Euclidean space"]:::fully_proved
n4["The hemispheres have compatible neighborhood deformation retractions"]:::fully_proved
n5("The reduced homology of spheres satisfies the suspension recurrence"):::fully_proved
n3 -.-> n4
n1 --> n3
n1 --> n2
n1 --> n4
n2 -.-> n4
n4 -.-> n5
n0 --> n4
n0 -.-> n5
click n0 "../../../../../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 n1 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#ordinary-neighborhood-mayer-vietoris" "The ordinary neighborhood-retract Mayer–Vietoris sequence — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#punctured-space-radial-deformation-retract" "A sphere strongly deformation retracts from punctured Euclidean space — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/homology/computations-and-applications/sphere-homology/index.html#closed-ball-radial-deformation-retract" "A closed ball strongly deformation retracts from Euclidean space — 1 item · 1 fully proved"
class n4 focus
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"
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"