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: van Kampen theorem | Statement: [Wirtinger presentation of knot groups, relatedTo, van Kampen theorem]

Target entity: van Kampen theorem
Context triple: [Wirtinger presentation of knot groups, relatedTo, van Kampen theorem]

• A. van Kampen diagram
  A van Kampen diagram is a planar, combinatorial 2-complex used in combinatorial group theory to visually represent relations in a group presentation and to prove that a word equals the identity.
• B. Eilenberg–MacLane spaces
  Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
• C. Hurewicz homomorphism
  The Hurewicz homomorphism is a fundamental map in algebraic topology that relates the homotopy groups of a space to its homology groups, often serving as a bridge between geometric and algebraic invariants.
• D. Künneth formula
  The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
• E. Foundations of Algebraic Topology
  Foundations of Algebraic Topology is a classic graduate-level textbook by Norman Steenrod that systematically develops the fundamental concepts and tools of algebraic topology.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: van Kampen theorem
Target entity description: The van Kampen theorem is a fundamental result in algebraic topology that computes the fundamental group of a space from the fundamental groups of overlapping subspaces and their intersections.

• A. van Kampen diagram
  A van Kampen diagram is a planar, combinatorial 2-complex used in combinatorial group theory to visually represent relations in a group presentation and to prove that a word equals the identity.
• B. Eilenberg–MacLane spaces
  Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
• C. Hurewicz homomorphism
  The Hurewicz homomorphism is a fundamental map in algebraic topology that relates the homotopy groups of a space to its homology groups, often serving as a bridge between geometric and algebraic invariants.
• D. Künneth formula
  The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
• E. Foundations of Algebraic Topology
  Foundations of Algebraic Topology is a classic graduate-level textbook by Norman Steenrod that systematically develops the fundamental concepts and tools of algebraic topology.
• F. None of above. chosen