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: [Henri Poincaré, notableWork, Poincaré–Lefschetz duality]

Target entity: Poincaré–Lefschetz duality
Context triple: [Henri Poincaré, notableWork, 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. 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.
• C. Atiyah–Singer index theorem
  The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
• D. Whitney approximation theorem
  The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
• E. Poincaré conjecture
  The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.