Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Poincaré–Hopf theorem | Statement: [Lefschetz fixed-point theorem, relatedTo, Poincaré–Hopf theorem]

Target entity: Poincaré–Hopf theorem
Context triple: [Lefschetz fixed-point theorem, relatedTo, Poincaré–Hopf theorem]

• A. Poincaré–Hopf theorem chosen
  The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
• B. Lefschetz fixed-point theorem
  The Lefschetz fixed-point theorem is a fundamental result in algebraic topology that relates the number of fixed points of a continuous map on a topological space to traces of the induced maps on its homology groups.
• C. Poincaré–Birkhoff fixed-point theorem
  The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
• D. Thom transversality theorem
  The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
• E. Atiyah–Bott fixed-point theorem
  The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.