Only the antipodal group acts freely on an even 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0("Coordinate sign changes on the sphere"):::fully_proved n1("A fixed-point-free sphere map has antipodal degree"):::fully_proved n2["Degree gives a character of a sphere action"]:::fully_proved n3("Only the antipodal group acts freely on an even sphere"):::fully_proved n1 -.-> n3 n2 --> n3 n0 --> n3 click n0 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#sphere-coordinate-sign-changes" "Coordinate sign changes on the sphere — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#fixed-point-free-degree" "A fixed-point-free sphere map has antipodal degree — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#sphere-action-degree-character" "Degree gives a character of a sphere action — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#free-even-sphere-action" "Only the antipodal group acts freely on an even sphere — 1 item · 1 fully proved"