Background prerequisites dependency map

Project map · Full theorem DAG · Open textbook chapter

This map contains the 14 decomposed items in this chapter. Dashed chapter boxes stand for external prerequisites or dependents.

fully proved3Proved, and every prerequisite is fully proved too.ready to state12Nothing it needs is blocked, so the statement can be written in Lean.planned14Described in the blueprint only.

graph LR n0("Balmer--Walter localization"):::can_state n1("Cech comparison"):::can_state n2("Classical reduction"):::can_state n3("Compact abelian Lie groups"):::can_state n4("Hardt triviality"):::can_state n5("Hatcher degree facts"):::can_state n6("Newman rigidity"):::can_state n7("Closed subgroups of $\Zp$"):::fully_proved n8("Serre odd-sphere maps"):::can_state n9("Sheaf cohomology bounds"):::can_state n10("Sheaf pushforward toolkit"):::can_state n11("Stacks derived facts"):::can_state n12("Symmetric forms and orthogonal sums"):::fully_proved n13("Verdier duality formalism"):::can_state n14["External chapter: Character classes and the contradiction 1 item · 1 planned"]:::boundary n15["External chapter: Preparing local tests 4 items · 1 fully proved · 3 planned"]:::boundary n16["External chapter: Localization, germs, and dense subcategories 1 item · 1 planned"]:::boundary n17["External chapter: Main theorems 3 items · 3 planned"]:::boundary n18["External chapter: Sheaf categories and homotopy invariance 4 items · 4 planned"]:::boundary n19["External chapter: A bounded lattice on the test sphere 2 items · 2 planned"]:::boundary n0 -.-> n16 n1 -. 2 .-> n15 n2 -.-> n17 n3 -.-> n17 n4 -.-> n19 n5 -.-> n19 n6 -.-> n15 n7 -. 3 .-> n15 n7 -.-> n17 n8 -.-> n15 n9 -.-> n14 n9 -.-> n18 n10 -. 3 .-> n18 n11 -.-> n14 n11 -.-> n15 n13 -. 3 .-> n18 click n0 "../../roadmap/background/index.html#balmer-walter" "Balmer--Walter localization — 1 item · 1 ready to state" click n1 "../../roadmap/background/index.html#cech-comparison" "Cech comparison — 1 item · 1 ready to state" click n2 "../../roadmap/background/index.html#classical-reduction" "Classical reduction — 1 item · 1 ready to state" click n3 "../../roadmap/background/index.html#compact-abelian-lie" "Compact abelian Lie groups — 1 item · 1 ready to state" click n4 "../../roadmap/background/index.html#hardt-triviality" "Hardt triviality — 1 item · 1 ready to state" click n5 "../../roadmap/background/index.html#hatcher-facts" "Hatcher degree facts — 1 item · 1 ready to state" click n6 "../../roadmap/background/index.html#newman-rigidity" "Newman rigidity — 1 item · 1 ready to state" click n7 "../../roadmap/background/index.html#padic-subgroups" "Closed subgroups of $\Zp$ — 1 item · 1 fully proved" click n8 "../../roadmap/background/index.html#serre-maps" "Serre odd-sphere maps — 1 item · 1 ready to state" click n9 "../../roadmap/background/index.html#sheaf-cohomology-bounds" "Sheaf cohomology bounds — 1 item · 1 ready to state" click n10 "../../roadmap/background/index.html#sheaf-pushforward" "Sheaf pushforward toolkit — 1 item · 1 ready to state" click n11 "../../roadmap/background/index.html#stacks-derived" "Stacks derived facts — 1 item · 1 ready to state" click n12 "../../roadmap/background/index.html#symmetric-forms" "Symmetric forms and orthogonal sums — 1 item · 1 fully proved" click n13 "../../roadmap/background/index.html#verdier-duality" "Verdier duality formalism — 1 item · 1 ready to state" click n14 "character-classes.html" "Character classes and the contradiction — 1 item · 1 planned" click n15 "local-tests.html" "Preparing local tests — 4 items · 1 fully proved · 3 planned" click n16 "localization.html" "Localization, germs, and dense subcategories — 1 item · 1 planned" click n17 "main-theorem.html" "Main theorems — 3 items · 3 planned" click n18 "sheaf-categories.html" "Sheaf categories and homotopy invariance — 4 items · 4 planned" click n19 "sphere-lattice.html" "A bounded lattice on the test sphere — 2 items · 2 planned"