The disjoint local pairs excise to the finite-puncture pair: 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 proved5Proved, and every prerequisite is fully proved too.planned1Described in the blueprint only.
graph LR
n0("Deleted-pair homology is local on an open neighborhood"):::fully_proved
n1["Disjoint punctured neighborhoods form the deleted union pair"]:::fully_proved
n2["A finite sphere-map fiber has disjoint isolated neighborhoods"]:::fully_proved
n3("The disjoint local pairs excise to the finite-puncture pair"):::fully_proved
n4["Finite-puncture homology is the coproduct of the local groups"]:::planned
n5("The finite-fiber pair map acts by the local degrees"):::fully_proved
n0 --> n3
n1 --> n3
n2 --> n3
n3 --> n5
n3 --> n4
click n0 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#deleted-pair-open-neighborhood" "Deleted-pair homology is local on an open neighborhood — 1 item · 1 fully proved"
click n1 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#disjoint-punctured-pair-iso" "Disjoint punctured neighborhoods form the deleted union pair — 1 item · 1 fully proved"
click n2 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-fiber-neighborhoods" "A finite sphere-map fiber has disjoint isolated neighborhoods — 1 item · 1 fully proved"
class n3 focus
click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-puncture-pair-excision" "The disjoint local pairs excise to the finite-puncture pair — 1 item · 1 fully proved"
click n4 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-puncture-homology-coproduct" "Finite-puncture homology is the coproduct of the local groups — 1 item · 1 planned"
click n5 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-fiber-local-map" "The finite-fiber pair map acts by the local degrees — 1 item · 1 fully proved"