Degree is the multiplier of the ordered sphere class: 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. fully proved7Proved, and every prerequisite is fully proved too.
graph LR
n0["The ordered class orients ordinary sphere homology"]:::fully_proved
n1("Degree is the multiplier of the ordered sphere class"):::fully_proved
n2("The formal properties of degree"):::fully_proved
n3("A sphere reflection has degree minus one"):::fully_proved
n4("A fixed-point-free sphere map has antipodal degree"):::fully_proved
n5("A nonsurjective sphere map has degree zero"):::fully_proved
n6("The finite-fiber pair map carries the global degree"):::fully_proved
n2 -.-> n3
n2 -.-> n4
n0 --> n1
n1 --> n2
n1 --> n3
n1 --> n4
n1 --> n5
n1 --> n6
click n0 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#integral-sphere-orientation" "The ordered class orients ordinary sphere homology — 1 item · 1 fully proved"
class n1 focus
click n1 "../../../../../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 n2 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#basic-degree-properties" "The formal properties of degree — 1 item · 1 fully proved"
click n3 "../../../../../roadmap/homology/computations-and-applications/degree/index.html#coordinate-reflection-degree" "A sphere reflection has degree minus one — 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#nonsurjective-degree-zero" "A nonsurjective sphere map has degree zero — 1 item · 1 fully proved"
click n6 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#global-degree-fiber-square" "The finite-fiber pair map carries the global degree — 1 item · 1 fully proved"