Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Oriented bordism groups of maps to a space
Definition
Let be a path-connected CW space. The oriented bordism set consists of classes of pairs , where is a closed smooth oriented -manifold and . Two pairs are bordant when there is a compact oriented -manifold with and a map restricting to and on the boundary. Disjoint union defines the operation. For a group , denotes a connected CW space with fundamental group and contractible universal cover.
Used by
- Casson–Gordon Witt class and signature defect Definition
- Torsion linking form and Casson–Gordon bordism data Definition
- Bordism independence of the Casson–Gordon Witt class Lemma
- Oriented bordism classes over a space form an abelian group Lemma
- Prime-power characters admit a multiple bounding bordism Lemma
- The relevant third oriented bordism group is finite Theorem
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Charles Livingston and Swatee Naik, Introduction to Knot Concordance (standard reference, not scraped)