Swapping the double simplex negates its fundamental class: 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.

graph LR n0["The ordered difference of the two simplices is a cycle"]:::fully_proved n1("The double-simplex difference generates reduced homology"):::fully_proved n2("Swapping the double simplex negates its fundamental class"):::fully_proved n3("Coordinate sign changes on the sphere"):::fully_proved n2 --> n3 n1 --> n2 n0 --> n2 n0 --> n1 click n0 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#double-simplex-fundamental-cycle" "The ordered difference of the two simplices is a cycle — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#double-simplex-fundamental-class" "The double-simplex difference generates reduced homology — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#double-simplex-swap-class" "Swapping the double simplex negates its fundamental class — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#sphere-coordinate-sign-changes" "Coordinate sign changes on the sphere — 1 item · 1 fully proved"