Finite-puncture homology is the coproduct of the local groups: 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 proved1Proved, and every prerequisite is fully proved too.planned3Described in the blueprint only.

graph LR n0["Relative homology commutes with coproducts of arbitrary pairs"]:::planned n1("The disjoint local pairs excise to the finite-puncture pair"):::fully_proved n2["Finite-puncture homology is the coproduct of the local groups"]:::planned n3("Finite-puncture projections have the diagonal matrix"):::planned n2 --> n3 n1 --> n2 n0 --> n2 click n0 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#relative-homology-sigma-pair" "Relative homology commutes with coproducts of arbitrary pairs — 1 item · 1 planned" click n1 "../../../../../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" class n2 focus click n2 "../../../../../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 n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-puncture-projection-matrix" "Finite-puncture projections have the diagonal matrix — 1 item · 1 planned"