The formal properties of 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 proved7Proved, and every prerequisite is fully proved too.ready to state1Prerequisites are stated, so this can be written down.

graph LR n0("Degree is the multiplier of the ordered sphere class"):::fully_proved n1("The formal properties of degree"):::fully_proved n2("A sphere reflection has degree minus one"):::fully_proved n3("The antipodal map has degree determined by dimension"):::fully_proved n4("A fixed-point-free sphere map has antipodal degree"):::fully_proved n5["Degree gives a character of a sphere action"]:::fully_proved n6("A nonvanishing tangent field forces odd dimension"):::fully_proved n7("A local homeomorphism has local degree plus or minus one"):::can_state n3 -.-> n4 n3 -.-> n6 n1 -.-> n3 n1 -.-> n2 n1 -.-> n4 n1 --> n5 n1 -.-> n6 n1 --> n7 n2 -.-> n3 n0 --> n1 n0 --> n2 n0 --> n4 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" class n1 focus 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#coordinate-reflection-degree" "A sphere reflection has degree minus one — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#antipodal-degree" "The antipodal map has degree determined by dimension — 1 item · 1 fully proved" click n4 "../../../../../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 n5 "../../../../../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" click n6 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#tangent-field-parity-obstruction" "A nonvanishing tangent field forces odd dimension — 1 item · 1 fully proved" click n7 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#homeomorphism-local-degree" "A local homeomorphism has local degree plus or minus one — 1 item · 1 ready to state"