The double simplex is a sphere: 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.

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["The standard simplex pair is homeomorphic to the disk pair"]:::fully_proved n3["The double simplex is a sphere"]:::fully_proved n4("Coordinate sign changes on the sphere"):::fully_proved n5["The ordered class orients ordinary sphere homology"]:::fully_proved n1 --> n3 n0 --> n1 n0 --> n3 n3 --> n5 n3 --> n4 n2 --> n3 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" click n2 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#standard-simplex-disk-pair-homeomorphism" "The standard simplex pair is homeomorphic to the disk pair — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../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" click n4 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#sphere-coordinate-sign-changes" "Coordinate sign changes on the sphere — 1 item · 1 fully proved" click n5 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#integral-sphere-orientation" "The ordered class orients ordinary sphere homology — 1 item · 1 fully proved"