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–Lefschetz duality | Statement: [Poincaré duality, generalizedBy, Poincaré–Lefschetz duality]

Target entity: Poincaré–Lefschetz duality
Context triple: [Poincaré duality, generalizedBy, Poincaré–Lefschetz duality]

• A. Poincaré duality chosen
  Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
• B. Mayer–Vietoris sequence in de Rham cohomology
  The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
• C. L’Analysis Situs et la Géométrie Algébrique
  L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
• D. 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.
• E. Poincaré–Hopf theorem
  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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.