Degree foundations and applications dependency map
This map shows the container's direct articles. Nested containers are collapsed and clickable; dependency edges are rolled up from their leaves. fully proved24Proved, and every prerequisite is fully proved too.ready to state1Prerequisites are stated, so this can be written down.
graph LR
n0("The antipodal map has degree determined by dimension"):::fully_proved
n1("The formal properties of degree"):::fully_proved
n2("A sphere reflection has degree minus one"):::fully_proved
n3("Swapping the double simplex negates its fundamental class"):::fully_proved
n4("A fixed-point-free sphere map has antipodal degree"):::fully_proved
n5("Only the antipodal group acts freely on an even sphere"):::fully_proved
n6["The ordered class orients ordinary sphere homology"]:::fully_proved
n7("A nonsurjective sphere map has degree zero"):::fully_proved
n8("A sphere has a nonvanishing tangent field exactly in odd dimension"):::fully_proved
n9["Odd spheres have a nonvanishing tangent field"]:::fully_proved
n10["A punctured sphere is Euclidean space"]:::fully_proved
n11["Degree gives a character of a sphere action"]:::fully_proved
n12("Coordinate sign changes on the sphere"):::fully_proved
n13("Degree is the multiplier of the ordered sphere class"):::fully_proved
n14("A nonvanishing tangent field forces odd dimension"):::fully_proved
n15["Tangent vector fields and normalization"]:::fully_proved
n16["External chapter: Homology<br/><small>9 items · 8 fully proved · 1 ready to state</small>"]:::boundary
n16 -->|2| n3
n16 -->|2| n6
n16 -.-> n7
n16 -.-> n10
n16 --> n12
n0 -.-> n4
n0 -.-> n14
n1 --> n16
n1 -.-> n0
n1 -.-> n2
n1 -.-> n4
n1 --> n11
n1 -.-> n14
n2 -.-> n0
n3 --> n12
n4 -.-> n5
n6 --> n16
n6 --> n13
n9 -.-> n8
n10 --> n16
n10 -.-> n7
n11 --> n5
n12 --> n0
n12 --> n2
n12 --> n5
n13 --> n16
n13 --> n1
n13 --> n2
n13 --> n4
n13 --> n7
n14 -.-> n8
n15 --> n8
n15 --> n9
n15 --> n14
click n0 "../../../../roadmap/homology/computations-and-applications/degree/index.html#antipodal-degree" "The antipodal map has degree determined by dimension — 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#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#double-simplex-swap-class" "Swapping the double simplex negates its fundamental class — 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#free-even-sphere-action" "Only the antipodal group acts freely on an even sphere — 1 item · 1 fully proved"
click n6 "../../../../roadmap/homology/computations-and-applications/degree/index.html#integral-sphere-orientation" "The ordered class orients ordinary sphere homology — 1 item · 1 fully proved"
click n7 "../../../../roadmap/homology/computations-and-applications/degree/index.html#nonsurjective-degree-zero" "A nonsurjective sphere map has degree zero — 1 item · 1 fully proved"
click n8 "../../../../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"
click n9 "../../../../roadmap/homology/computations-and-applications/degree/index.html#odd-sphere-tangent-field" "Odd spheres have a nonvanishing tangent field — 1 item · 1 fully proved"
click n10 "../../../../roadmap/homology/computations-and-applications/degree/index.html#punctured-sphere-stereographic" "A punctured sphere is Euclidean space — 1 item · 1 fully proved"
click n11 "../../../../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 n12 "../../../../roadmap/homology/computations-and-applications/degree/index.html#sphere-coordinate-sign-changes" "Coordinate sign changes on the sphere — 1 item · 1 fully proved"
click n13 "../../../../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 n14 "../../../../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 n15 "../../../../roadmap/homology/computations-and-applications/degree/index.html#tangent-vector-field-data" "Tangent vector fields and normalization — 1 item · 1 fully proved"
click n16 "../../../chapters/homology.html" "Homology — 9 items · 8 fully proved · 1 ready to state"