A nonvanishing tangent field forces odd dimension: 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("The formal properties of degree"):::fully_proved n1("The antipodal map has degree determined by dimension"):::fully_proved n2["Tangent vector fields and normalization"]:::fully_proved n3("A nonvanishing tangent field forces odd dimension"):::fully_proved n4("A sphere has a nonvanishing tangent field exactly in odd dimension"):::fully_proved n1 -.-> n3 n0 -.-> n1 n0 -.-> n3 n3 -.-> n4 n2 --> n4 n2 --> n3 click n0 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#basic-degree-properties" "The formal properties of degree — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#antipodal-degree" "The antipodal map has degree determined by dimension — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#tangent-vector-field-data" "Tangent vector fields and normalization — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../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 n4 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#nonzero-tangent-field-iff-odd" "A sphere has a nonvanishing tangent field exactly in odd dimension — 1 item · 1 fully proved"