Novikov’s higher signature conjecture

Target entity: Novikov’s higher signature conjecture
Context triple: [Sergei Novikov, knownFor, Novikov’s higher signature conjecture]

• A. Hirzebruch signature theorem
  The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
• B. 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.
• 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. The geometry of four-manifolds
  The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
• E. Hopf conjecture (on Euler characteristic and curvature)
  The Hopf conjecture on Euler characteristic and curvature is an open problem in differential geometry proposing a deep link between the sign of a manifold’s Euler characteristic and the sign of its sectional curvature, especially for even-dimensional manifolds with positive or negative curvature.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Novikov’s higher signature conjecture
Target entity description: Novikov’s higher signature conjecture is a major open problem in topology asserting that certain higher signatures of manifolds are homotopy invariants, linking manifold topology with operator algebras and index theory.

• A. Hirzebruch signature theorem
  The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
• B. 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.
• 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. The geometry of four-manifolds
  The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
• E. Hopf conjecture (on Euler characteristic and curvature)
  The Hopf conjecture on Euler characteristic and curvature is an open problem in differential geometry proposing a deep link between the sign of a manifold’s Euler characteristic and the sign of its sectional curvature, especially for even-dimensional manifolds with positive or negative curvature.
• F. None of above. chosen