h-principle in geometry

Target entity: h-principle in geometry
Context triple: [Mikhail Gromov, notableFor, h-principle in geometry]

• A. Smale–Hirsch immersion theorem
  The Smale–Hirsch immersion theorem is a fundamental result in differential topology that classifies immersions of manifolds up to regular homotopy in terms of bundle monomorphisms between their tangent bundles.
• B. Thom transversality theorem
  The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
• C. 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.
• D. Introduction to Symplectic Topology
  Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
• E. Nash embedding theorem
  The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: h-principle in geometry
Target entity description: The h-principle in geometry is a foundational concept introduced by Mikhail Gromov that relates solutions of differential relations to their homotopy-theoretic counterparts, often allowing geometric problems to be reduced to purely topological ones.

• A. Smale–Hirsch immersion theorem
  The Smale–Hirsch immersion theorem is a fundamental result in differential topology that classifies immersions of manifolds up to regular homotopy in terms of bundle monomorphisms between their tangent bundles.
• B. Thom transversality theorem
  The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
• C. 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.
• D. Introduction to Symplectic Topology
  Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
• E. Nash embedding theorem
  The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
• F. None of above. chosen