The neighborhood quotient map preserves relative homology: 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0["Deleted-subset excision induces homology isomorphisms"]:::fully_proved n1["The complementary excision diagram"]:::fully_proved n2["The neighborhood quotient map preserves relative homology"]:::fully_proved n3("Good-pair relative homology is reduced quotient homology"):::fully_proved n1 -.-> n3 n1 --> n2 n2 -.-> n3 n0 --> n1 n0 -.-> n2 click n0 "../../../../../../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" click n1 "../../../../../../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" class n2 focus click n2 "../../../../../../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 n3 "../../../../../../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"