A sphere has a nonvanishing tangent field exactly in 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0["Tangent vector fields and normalization"]:::fully_proved n1("A nonvanishing tangent field forces odd dimension"):::fully_proved n2["Odd spheres have a nonvanishing tangent field"]:::fully_proved n3("A sphere has a nonvanishing tangent field exactly in odd dimension"):::fully_proved n2 -.-> n3 n1 -.-> n3 n0 --> n3 n0 --> n2 n0 --> n1 click n0 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#tangent-vector-field-data" "Tangent vector fields and normalization — 1 item · 1 fully proved" click n1 "../../../../../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 n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#odd-sphere-tangent-field" "Odd spheres have a nonvanishing tangent field — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../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"