The complementary excision diagram: 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 proved7Proved, and every prerequisite is fully proved too.

graph LR n0["Topology of the point-quotient projection"]:::fully_proved n1("Restricting the quotient to a good-pair neighborhood"):::fully_proved n2["Enlarging to the chosen neighborhood preserves relative homology"]:::fully_proved n3["Deleted-subset excision induces homology isomorphisms"]:::fully_proved n4["The complementary excision diagram"]:::fully_proved n5["The neighborhood quotient map preserves relative homology"]:::fully_proved n6("Good-pair relative homology is reduced quotient homology"):::fully_proved n4 -.-> n6 n4 --> n5 n1 --> n4 n2 --> n4 n2 -.-> n6 n5 -.-> n6 n0 --> n4 n0 --> n1 n3 --> n4 n3 -.-> n5 click n0 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#point-quotient-projection-topology" "Topology of the point-quotient projection — 1 item · 1 fully proved" click n1 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-neighborhood-quotient" "Restricting the quotient to a good-pair neighborhood — 1 item · 1 fully proved" click n2 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-neighborhood-relative-homology" "Enlarging to the chosen neighborhood preserves relative homology — 1 item · 1 fully proved" click n3 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#deleted-subset-excision-homology-isomorphism" "Deleted-subset excision induces homology isomorphisms — 1 item · 1 fully proved" class n4 focus click n4 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-excision-diagram" "The complementary excision diagram — 1 item · 1 fully proved" click n5 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#point-quotient-neighborhood-excision" "The neighborhood quotient map preserves relative homology — 1 item · 1 fully proved" click n6 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-point-quotient-relative-homology" "Good-pair relative homology is reduced quotient homology — 1 item · 1 fully proved"