Enlarging the quotient point 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. fully proved6Proved, and every prerequisite is fully proved too.
graph LR
n0("Restricting the quotient to a good-pair neighborhood"):::fully_proved
n1("Componentwise isomorphisms imply a relative isomorphism"):::fully_proved
n2["A homotopy equivalence induces homology isomorphisms"]:::fully_proved
n3["The quotient neighborhood contracts to its point"]:::fully_proved
n4["Enlarging the quotient point preserves relative homology"]:::fully_proved
n5("Good-pair relative homology is reduced quotient homology"):::fully_proved
n2 -.-> n4
n0 --> n3
n0 --> n4
n3 -.-> n4
n4 -.-> n5
n1 -.-> n4
click n0 "../../../../../../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 n1 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#relative-homology-map-isomorphism-criterion" "Componentwise isomorphisms imply a relative isomorphism — 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/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#point-quotient-neighborhood-contraction" "The quotient neighborhood contracts to its point — 1 item · 1 fully proved"
class n4 focus
click n4 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#point-quotient-neighborhood-relative-homology" "Enlarging the quotient point preserves relative homology — 1 item · 1 fully proved"
click n5 "../../../../../../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"