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: Lefschetz fixed-point theorem | Statement: [Hard Lefschetz theorem, isRelatedTo, Lefschetz fixed-point theorem]

Target entity: Lefschetz fixed-point theorem
Context triple: [Hard Lefschetz theorem, isRelatedTo, Lefschetz fixed-point theorem]

• A. Lefschetz fixed-point theorem chosen
  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.
• B. Lefschetz number
  The Lefschetz number is a topological invariant, computed from the traces of induced maps on homology, that predicts the existence and number of fixed points of a continuous self-map on a topological space.
• C. 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.
• D. 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.
• E. Brouwer fixed-point theorem
  The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.