The ordered class orients ordinary sphere 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 proved5Proved, and every prerequisite is fully proved too.

graph LR n0["Reduced and ordinary homology agree in positive degrees"]:::fully_proved n1["The double simplex is a sphere"]:::fully_proved n2["The ordered class orients ordinary sphere homology"]:::fully_proved n3("Degree is the multiplier of the ordered sphere class"):::fully_proved n4["The ordered sphere class orients local homology"]:::fully_proved n2 --> n3 n2 --> n4 n1 --> n2 n0 --> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#reduced-positive-degree-comparison" "Reduced and ordinary homology agree in positive degrees — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#double-simplex-sphere-homeomorphism" "The double simplex is a sphere — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#integral-sphere-orientation" "The ordered class orients ordinary sphere homology — 1 item · 1 fully proved" click n3 "../../../../../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 n4 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#sphere-local-orientation" "The ordered sphere class orients local homology — 1 item · 1 fully proved"