The ordinary neighborhood-retract Mayer–Vietoris sequence: 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 proved9Proved, and every prerequisite is fully proved too.

graph LR n0("The standard cover of a well-pointed wedge"):::fully_proved n1["Strong deformation retracts"]:::fully_proved n2["A homotopy equivalence induces homology isomorphisms"]:::fully_proved n3("The binary-cover Mayer–Vietoris sequence"):::fully_proved n4("The ordinary neighborhood-retract Mayer–Vietoris sequence"):::fully_proved n5["A sphere strongly deformation retracts from punctured Euclidean space"]:::fully_proved n6("The reduced neighborhood-retract Mayer–Vietoris sequence"):::fully_proved n7["A closed ball strongly deformation retracts from Euclidean space"]:::fully_proved n8["The hemispheres have compatible neighborhood deformation retractions"]:::fully_proved n0 --> n4 n3 --> n4 n7 -.-> n8 n4 --> n7 n4 --> n5 n4 --> n6 n4 --> n8 n5 -.-> n8 n2 -.-> n4 n1 --> n4 click n0 "../../../../../roadmap/fundamental-group/van-kampen/index.html#well-pointed-wedge-cover" "The standard cover of a well-pointed wedge — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#strong-deformation-retract" "Strong deformation retracts — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/simplicial-and-singular/index.html#homotopy-equivalence-homology-iso" "A homotopy equivalence induces homology isomorphisms — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#binary-cover-mayer-vietoris-sequence" "The binary-cover Mayer–Vietoris sequence — 1 item · 1 fully proved" class n4 focus click n4 "../../../../../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 n5 "../../../../../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 n6 "../../../../../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 n7 "../../../../../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" click n8 "../../../../../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"