DefinitionDefinition: Literature-sourcedProof: Literature-sourced

How 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.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Limitwise-nullhomotopy subgroup of a leaf

Definition

Assume Countable Choice ${A C}_{ω}$ . For a transversely oriented codimension- one foliation, a leaf $L$ , a base point $x \in L$ , and a side $j$ , define $Π_{1}^{j} (L, x)$ to be the set of classes $[α] \in N_{j} (L, x)$ for which the predicate $Q_{j} (f)$ of Limitwise-nullhomotopy predicate on based loops holds for a based representative $f$ . By Limitwise-nullhomotopy predicate descends to a normal subgroup, this is independent of the representative and fence and is a normal subgroup of $π_{1} (L, x)$ . It is Novikov’s limitwise-nullhomotopy subgroup, distinct from the ordinary limit-cycle quotient $P_{j}$ .

Depends on

Used by

Dependency tree · two levels

16 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

S. P. Novikov, The Topology of Foliations (English translation by J. A. Zilber; complete PDF of the translation) (standard reference, not scraped)