A fixed-point-free sphere map has antipodal 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 proved5Proved, and every prerequisite is fully proved too.

graph LR n0("Degree is the multiplier of the ordered sphere class"):::fully_proved n1("The formal properties of degree"):::fully_proved n2("The antipodal map has degree determined by dimension"):::fully_proved n3("A fixed-point-free sphere map has antipodal degree"):::fully_proved n4("Only the antipodal group acts freely on an even sphere"):::fully_proved n2 -.-> n3 n1 -.-> n2 n1 -.-> n3 n3 -.-> n4 n0 --> n1 n0 --> 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/degree/index.html#basic-degree-properties" "The formal properties of degree — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#antipodal-degree" "The antipodal map has degree determined by dimension — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../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 n4 "../../../../../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"