The finite-fiber pair map carries the global degree: 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.planned2Described in the blueprint only.

graph LR n0("Degree is the multiplier of the ordered sphere class"):::fully_proved n1["The ordered sphere class orients local homology"]:::fully_proved n2["A finite sphere-map fiber has disjoint isolated neighborhoods"]:::fully_proved n3("The finite-fiber pair map carries the global degree"):::fully_proved n4("The finite-puncture class is the sum of the local classes"):::planned n5("Degree is the sum of the local degrees"):::planned n0 --> n3 n2 --> n3 n4 --> n5 n3 --> n5 n3 --> n4 n1 --> n4 n1 --> n3 click n0 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#sphere-degree-definition" "Degree is the multiplier of the ordered sphere class — 1 item · 1 fully proved" click n1 "../../../../../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 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#global-degree-fiber-square" "The finite-fiber pair map carries the global degree — 1 item · 1 fully proved" click n4 "../../../../../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 n5 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#degree-local-sum-formula" "Degree is the sum of the local degrees — 1 item · 1 planned"