The ordered sphere class orients local 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 proved6Proved, and every prerequisite is fully proved too.planned1Described in the blueprint only.

graph LR n0["A contractible subspace identifies reduced and relative homology"]:::fully_proved n1["The ordered class orients ordinary sphere homology"]:::fully_proved n2["A punctured sphere is Euclidean space"]:::fully_proved n3["The ordered sphere class orients local homology"]:::fully_proved n4("The finite-fiber pair map carries the global degree"):::fully_proved n5("The finite-puncture class is the sum of the local classes"):::planned n6("Local degree on a chosen isolated neighborhood"):::fully_proved n1 --> n3 n2 --> n3 n4 --> n5 n3 --> n5 n3 --> n4 n3 --> n6 n0 --> n3 click n0 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#contractible-subspace-relative-reduced-homology" "A contractible subspace identifies reduced and relative homology — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#integral-sphere-orientation" "The ordered class orients ordinary sphere homology — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#punctured-sphere-stereographic" "A punctured sphere is Euclidean space — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#sphere-local-orientation" "The ordered sphere class orients local homology — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#global-degree-fiber-square" "The finite-fiber pair map carries the global degree — 1 item · 1 fully proved" click n5 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#finite-puncture-orientation-sum" "The finite-puncture class is the sum of the local classes — 1 item · 1 planned" click n6 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#neighborhood-local-degree" "Local degree on a chosen isolated neighborhood — 1 item · 1 fully proved"