On embeddings of spheres

Target entity: On embeddings of spheres
Context triple: [Barry Mazur, doctoralThesis, On embeddings of spheres]

• 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. 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.
• C. Whitney embedding theorem
  The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
• D. Thom cobordism theory
  Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: On embeddings of spheres
Target entity description: "On embeddings of spheres" is Barry Mazur's influential doctoral thesis in topology, focusing on the study of how spheres can be embedded in higher-dimensional manifolds.

• 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. 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.
• C. Whitney embedding theorem
  The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
• D. Thom cobordism theory
  Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
• E. 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.
• F. None of above. chosen